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Math Problems
Grade 8
Write linear functions: word problems
Henry bought an electric guitar which was advertised at
$
1280
\$1280
$1280
excluding GST. If the GST rate was
7
%
7\%
7%
, calculate
\newline
(a) the amount of GST he paid,
\newline
(b) the price of the guitar inclusive of GST.
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Brendan walked his dog
b
b
b
blocks in the morning and
6
6
6
blocks in the afternoon. Write an expression that shows the number of blocks Brendan walked his dog in all.
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Prepare
0.5
M
0.5\,\text{M}
0.5
M
in of
NaCl
\text{NaCl}
NaCl
in a
(
volumetric flask
)
ml
(\text{volumetric flask})\,\text{ml}
(
volumetric flask
)
ml
of water ?
M.Wt
\text{M.Wt}
M.Wt
Na
=
23
g/mol
\text{Na}=23\,\text{g/mol}
Na
=
23
g/mol
Cl
=
35.5
g/mole
\text{Cl}=35.5\,\text{g/mole}
Cl
=
35.5
g/mole
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C
=
40
(
5
−
s
)
C = 40( 5 - s )
C
=
40
(
5
−
s
)
After Hiro's family photoshoot, the photographer sells the printed photos by the sheet. Hiro has a
$
200
\$200
$200
credit from a prior session, and the equation gives the total credit left,
C
C
C
, in dollars, if he buys
s
s
s
sheets. How many sheets can Hiro purchase with his credit?
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(A)
3
3
3
\newline
At the same rate,
$
9
\$ 9
$9
can buy
\newline
(B)
4
4
4
bagels.
\newline
(C)
6
6
6
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Frank had
$
65
\$65
$65
.He spent
$
2
\$2
$2
per day for
7
7
7
days.Then he was given
$
9
\$9
$9
to divide equally between himself and his
2
2
2
brothers.What expression can be used to find the amount of money frank had remaining?
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There are
180
180
180
students at Oaktown Middle School who play instruments. This is
60
%
60 \%
60%
of the total number of students.
\newline
(a) Draw a double number line that can be used to find the total number of students at the school.
\newline
(b) What is the total number of students at the school?
\newline
□
\square
□
students
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Question
\newline
Watch Video
\newline
Show Examples
\newline
Find the equation of a line perpendicular to
2
x
−
2
y
=
2
2 x-2 y=2
2
x
−
2
y
=
2
that passes through the point
(
−
1
,
4
)
(-1,4)
(
−
1
,
4
)
.
\newline
Answer
\newline
y
−
4
=
−
(
x
+
1
)
y-4=-(x+1)
y
−
4
=
−
(
x
+
1
)
\newline
y
+
4
=
−
(
x
−
1
)
y+4=-(x-1)
y
+
4
=
−
(
x
−
1
)
\newline
y
−
4
=
x
+
1
y-4=x+1
y
−
4
=
x
+
1
\newline
y
+
4
=
x
−
1
y+4=x-1
y
+
4
=
x
−
1
\newline
Submit Answer
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The demand function for a certain USB key is
p
=
490
−
6
x
p = 490 - 6x
p
=
490
−
6
x
, where
p
p
p
is the price (in
$
\$
$
) per unit and
x
x
x
is the number of units (in thousands), and the supply function is
p
=
1130
+
18
x
p = 1130 + 18x
p
=
1130
+
18
x
. Determine the consumer's and the producer's surplus when the market unit price is set at the equilibrium price
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How many moles of hydrogen,
H
H
H
, are needed to react with
3.0
3.0
3.0
moles of nitrogen,
N
2
N_2
N
2
?
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A bank efficiency ratio is the ratio of a bank's expenses to its revenue, expressed as a percentage. If a bank has
$
222
\$222
$222
million dollars in expenses and an efficiency ratio of
75
%
75\%
75%
, what is its revenue in millions of dollars?
\newline
◻
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100
−
10
m
100-10m
100
−
10
m
\newline
Dante's goal this year is to read
100
100
100
books. The expression above models the number of books Dante has left to read $m months after the beginning of the year. Based on the expression, how many books does Dante have left to read after
4
4
4
months?
\newline
◻
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Alex learned
80
80
80
new vocabulary words for his English exam. The following function gives the number of words he remembers after
t
t
t
days:
\newline
W
(
t
)
=
80
(
1
−
0.1
t
)
3
W(t)=80(1-0.1 t)^{3}
W
(
t
)
=
80
(
1
−
0.1
t
)
3
\newline
What is the instantaneous rate of change of the number of words Alex remembers after
5
5
5
days?
\newline
Choose
1
1
1
answer:
\newline
(A)
10
\mathbf{1 0}
10
days
\newline
(B)
10
\mathbf{1 0}
10
words per day
\newline
(C)
−
6
-6
−
6
days
\newline
(D)
−
6
-6
−
6
words per day
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A water tank is drained. The following function gives the volume, in liters, of the water remaining in the tank
t
t
t
minutes after the drain is opened:
\newline
V
(
t
)
=
3000
(
1
−
0.05
t
)
2
V(t)=3000(1-0.05 t)^{2}
V
(
t
)
=
3000
(
1
−
0.05
t
)
2
\newline
What is the instantaneous rate of change of the volume after
10
10
10
minutes?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
150
-150
−
150
liters per minute
\newline
(B)
−
150
-150
−
150
minutes per liter
\newline
(C)
750
750
750
liters per minute
\newline
(D)
750
750
750
minutes per liter
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Kajal holds a ruler in some wavy water. The depth of the water
t
t
t
seconds after she starts measuring it, in
c
m
\mathrm{cm}
cm
, is given by
\newline
D
(
t
)
=
50
−
23
sin
(
π
(
t
+
0.23
)
)
.
D(t)=50-23 \sin (\pi(t+0.23)) .
D
(
t
)
=
50
−
23
sin
(
π
(
t
+
0.23
))
.
\newline
After she starts measuring, when is the first time the depth of the waves is at its average value? Give an exact answer.
\newline
When
t
=
□
t= \square
t
=
□
seconds
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Find the surface area of the rectangular prism.
\newline
Area of Irregutar Shapes
\newline
Surtace Area of Rectangular Prisms
\newline
Volume of Rectangular Prisms
\newline
Answer Antempt
2
2
2
out of
2
2
2
\newline
y
d
2
y d^{2}
y
d
2
\newline
submit Ansurs
\newline
Subretit Ansmer
\newline
Caloulator
\newline
Stial Spxk?
\newline
Log Out
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Topic
9
9
9
: Readiness Assessme
\newline
[s] Savvas Realize
\newline
GEOMEIRY SPRING
2
2
2
ND BLOCK
\newline
Topic
9
9
9
: Readiness Assessment
\newline
Find each slope. Round to the nearest tenth.
\newline
slope of
c
=
c=
c
=
\newline
slope of
e
=
e=
e
=
\newline
slope of
d
=
d=
d
=
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20
20
20
. Tim takes his pulse for
10
s
e
c
10 \mathrm{sec}
10
sec
and counts
12
12
12
beats. How many beats per minute is this?
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Pedro conducted taste tests of a beverage recipe containing different amounts of a secret ingredient. The graph in the
q
p
q p
qp
-plane relates the quantity,
q
q
q
, of a secret ingredient, in ounces per gallon of the beverage, to the percent,
p
p
p
, of taste testers who approved that recipe. What is the best interpretation of the labeled point, the highest on the graph, in terms of Pedro's taste test results?
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and
$
20
\$ 20
$20
per hour of labor. Write and solve an equation to find the number of labor hours you were charged.
\qquad
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Suppose the total
cost
C
(
x
)
\operatorname{cost} C(x)
cost
C
(
x
)
(in dollars) to manufacture a quantity
x
x
x
of weed killer (in hundreds of liters) is given by the function
C
(
x
)
=
x
3
−
3
x
2
+
9
x
+
40
C(x)=x^{3}-3 x^{2}+9 x+40
C
(
x
)
=
x
3
−
3
x
2
+
9
x
+
40
, where
x
>
0
x>0
x
>
0
.
\newline
a) Where is
C
(
x
)
\mathrm{C}(\mathrm{x})
C
(
x
)
decreasing?
\newline
b) Where is
C
(
x
)
\mathrm{C}(\mathrm{x})
C
(
x
)
increasing?
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Use trigonometry to find the missing
s
s
s
F
=
F=
F
=
F
E
E
=
\quad FEE =
FEE
=
\quad
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Tou want to heve a
$
100
,
000
\$ 100,000
$100
,
000
college fund in
20
20
20
years. How much will you have to deposit now in an account with an APR of
5
%
5 \%
5%
and dally compounding?
\newline
P
=
A
(
1
+
(
A
P
R
n
)
)
n
y
P=\frac{A}{\left(1+\left(\frac{A P R}{n}\right)\right)^{n y}}
P
=
(
1
+
(
n
A
PR
)
)
n
y
A
\newline
$
35
,
950.49
\$ 35,950.49
$35
,
950.49
\newline
$
36.794.39
\$ 36.794 .39
$36.794.39
\newline
$
36
,
790.46
\$ 36,790.46
$36
,
790.46
\newline
$
38
,
940.29
\$ 38,940.29
$38
,
940.29
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Wegmans Bakery produces cheesecake for sale. The bakery, which operates
5
5
5
days per week and
52
52
52
weeks per year, can produce
40
40
40
cakes per day. The bakery sets up cake production operation and produces the predetermined quantity
Q
Q
Q
has been produced. The setup cost for a production run of cheesecake is
$
250
\$250
$250
. The holding cost is
$
5
\$5
$5
per year. The annual demand for cheesecake is constant during the year and is equal to
3900
3900
3900
. Determine the following: Round answers to the nearest whole number. (a) the optimal production run quantity (
Q
Q
Q
). (b) the total annual inventory cost (
A
H
C
+
A
O
C
AHC + AOC
A
H
C
+
A
OC
). (c) the optimal number of production runs per year. (d) The run length (production run time).
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NCS Bookmarks
\newline
24
24
24
\newline
My IXL
\newline
Learning
\newline
Ass
\newline
Geometry > G.
4
4
4
Review: interior and exterior angles of polygons
6
6
6
VG
\newline
The diagram shows a convex polygon.
\newline
What is the value of
v
v
v
?
\newline
v
=
v=
v
=
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QUADRATIC EQUATIONS
\newline
5
5
5
. An express train takes
1
1
1
hour less than a passenger train to travel
132
k
m
132 \mathrm{~km}
132
km
between Mysore and Bangalore. If the average speed of the express train is
11
k
m
/
h
r
11 \mathrm{~km} / \mathrm{hr}
11
km
/
hr
more than that of the passenger train, form the quadratic equation to find the average speed of express train.
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Raymond just got done jumping at Super Bounce Trampoline Center. The total cost of his session was
$
43.25
\$ 43.25
$43.25
. He had to pay a
$
7
\$ 7
$7
entrance fee and
$
1.25
\$ 1.25
$1.25
for every minute he was on the trampoline.
\newline
Write an equation to determine the number of minutes
(
t
)
(t)
(
t
)
that Raymond was on the trampoline.
\newline
Find the number of minutes he was on the trampoline.
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p
(
x
)
=
(
x
−
0.95
)
(
500
−
100
x
)
p(x)=(x-0.95)(500-100 x)
p
(
x
)
=
(
x
−
0.95
)
(
500
−
100
x
)
\newline
The equation models
p
p
p
, the daily profit, in dollars, a food truck makes by selling their signature tacos at a price of
x
x
x
dollars each. What is the daily profit if the tacos are sold at
$
3
\$ 3
$3
each?
\newline
Choose
1
1
1
answer:
\newline
(A)
$
410
\$ 410
$410
\newline
(B)
$
600
\$ 600
$600
\newline
(C)
$
820
\$ 820
$820
\newline
(D)
$
2
,
460
\$ 2,460
$2
,
460
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A caterpillar eats
1400
%
1400 \%
1400%
of its birth mass in one day. The caterpillar's birth mass is
m
m
m
grams.
\newline
Which of the following expressions could represent the amount, in grams, the caterpillar eats in one day?
\newline
Choose
2
2
2
answers:
\newline
A
14
m
14 m
14
m
\newline
B
1400
100
m
\frac{1400}{100} m
100
1400
m
\newline
C
140
m
140 \mathrm{~m}
140
m
\newline
D
1400
m
1400 m
1400
m
\newline
E
1.4
m
1.4 m
1.4
m
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The sum of the ages of a man and his wife is
81
81
81
years. The ratio of their ages is
5
:
4
5:4
5
:
4
. Find the age of the younger person.
\newline
A.
30
30
30
years
\newline
B.
36
36
36
years
\newline
C.
45
45
45
years
\newline
D.
51
51
51
years
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The sum of the ages of a man and his wife is \(81 years. The ratio of their ages is
5
:
4
5: 4
5
:
4
. Find the age of the younger person.
\newline
A.
30
30
30
years
\newline
B.
36
36
36
years
\newline
C.
45
45
45
years
\newline
D.
51
51
51
years
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P
=
19
2
+
4
25
d
P=\frac{19}{2}+\frac{4}{25} d
P
=
2
19
+
25
4
d
\newline
The amount of paint,
P
P
P
, in pints, that an art studio can buy with
d
d
d
dollars is given by the equation. What is the best interpretation of
4
25
\frac{4}{25}
25
4
as shown in the equation?
\newline
Choose
1
1
1
answer:
\newline
(A) The paint costs
4
25
\frac{4}{25}
25
4
of a dollar per pint.
\newline
B) One dollar can buy
4
25
\frac{4}{25}
25
4
of a pint of paint.
\newline
5
5
5
of
10
10
10
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Point
X
\mathrm{X}
X
is located at
−
14
-14
−
14
. Point
Y
\mathrm{Y}
Y
is
6
6
6
less than Point
X
\mathrm{X}
X
. Where is
Y
\mathrm{Y}
Y
located?
\newline
Y
=
□
Y= \square
Y
=
□
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Point A is located at
−
19
-19
−
19
. Point
B
\mathrm{B}
B
is
6
6
6
less than Point
A
\mathrm{A}
A
. Where is
B
\mathrm{B}
B
located?
\newline
B
=
□
B= \square
B
=
□
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Tyshawn was out at a restaurant for dinner when the bill came. He wanted to leave a tip of
28
%
28 \%
28%
. What number should he multiply the cost of the meal by to find the total plus tip in one step?
\newline
Answer:
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The weight,
w
w
w
, in ounces, of a glass soda bottle design with a side length of
l
l
l
inches is given by the equation. By how many ounces does the weight of the bottle increase for every inch of increase in the side length?
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Larry is on his school's cross-country team. He runs
8
8
8
miles during each practice. Write an equation that shows the relationship between the number of practices Larry attends,
x
x
x
, and the total number of miles he runs,
y
y
y
.
\newline
y = ____
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The formula for the distance traveled over time
t
t
t
and at an average speed
v
v
v
is
d
=
v
×
t
d = v \times t
d
=
v
×
t
. Amit ran for
40
40
40
minutes at a speed of about
5
5
5
kilometers per hour. What calculation will give us the estimated distance Amit ran in kilometers?
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The formula for the distance traveled over time
t
t
t
and at an average speed
v
v
v
is
d
=
v
×
t
d = v \times t
d
=
v
×
t
. Amit ran for
45
45
45
minutes at a speed of about
10
10
10
kilometers per hour. What calculation will give us the estimated distance Amit ran in kilometers?
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g
=
15
−
m
32
g=15-\frac{m}{32}
g
=
15
−
32
m
\newline
If Vera starts with a full tank of gas, the number of gallons of gas,
g
g
g
, left in the tank after driving
m
m
m
miles is given by the equation. When full, how many gallons of gas does Vera's tank hold?
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\newline
1
2
\frac{1}{2}
2
1
\newline
Correct
\newline
ω
=
k
m
\omega=\sqrt{\frac{k}{m}}
ω
=
m
k
. This is the formula for the angular frequency
\newline
ω
\omega
ω
of a mass
\newline
m
m
m
suspended from a spring of spring constant
\newline
k
k
k
. Solve this formula for
\newline
k
k
k
\newline
Answer
\newline
Keyboar
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In an ATM if the currency notes of denominations of Rs.
500
500
500
, Rs.
100
100
100
and Rs.
50
50
50
respectively the notes are in the ratio of
3
:
3
:
4
3:3:4
3
:
3
:
4
. The total cash in the ATM is Rs.
400
,
000
400,000
400
,
000
. How many notes of each denominations that ATM contains?
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Seb bikes at a constant rate of
20
20
20
kilometers per hour.
1
1
1
. Write an equation that represents the distance, in kilometers, Seb travels
(
b
)
(b)
(
b
)
based on how many hours he bikes
(
t
)
(t)
(
t
)
at this rate.
2
2
2
. How far will Seb travel if he bikes at this rate for
3
3
3
hours?
_
\_
_
kilometers
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Jessica received a
$
40.50
\$40.50
$40.50
gift card for a photo center. She used it to buy prints that cost
7
7
7
cents each. The remaining balance,
B
B
B
(in dollars), on the card after buying
x
x
x
prints is given by the following function. What is the remaining balance on the card if Jessica bought
40
40
40
prints?
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P
(
t
)
=
20
(
0.95
)
t
P(t)=20(0.95)^t
P
(
t
)
=
20
(
0.95
)
t
\newline
The function models
P
P
P
, the population of Leetown in thousands,
t
t
t
years after
2007
2007
2007
. What was the population of Leetown in
2007
2007
2007
?
\newline
Choose
1
1
1
answer:
\newline
(A)
\text{(A)}
(A)
5
5
5
thousand
\newline
(B)
\text{(B)}
(B)
19
19
19
thousand
\newline
(C)
\text{(C)}
(C)
20
20
20
thousand
\newline
(D)
\text{(D)}
(D)
95
95
95
thousand
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Montraie goes to a restaurant and the subtotal on the bill was
x
x
x
dollars. A tax of
7
%
7 \%
7%
is applied to the bill. Montraie decides to leave a tip of
21
%
21 \%
21%
on the entire bill (including the tax). Write an expression in terms of
x
x
x
that represents the total amount that Montraie paid.
\newline
Answer:
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To get the
10
%
10 \%
10%
discount, a shopper must spend at least
$
500
\$ 500
$500
.
\newline
Use
d
d
d
to represent the spending (in dollars) of a shopper who gets the discount.
\newline
d
≥
500
d \geq 500
d
≥
500
\newline
Continue
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P
=
19
2
+
4
25
d
P=\frac{19}{2}+\frac{4}{25} d
P
=
2
19
+
25
4
d
\newline
The amount of paint,
P
P
P
, in pints, that an art studio can buy with
d
d
d
dollars is given by the equation. What is the best interpretation of
4
25
\frac{4}{25}
25
4
as shown in the equation?
\newline
Choose
1
1
1
answer:
\newline
(A) The paint costs
4
25
\frac{4}{25}
25
4
of a dollar per pint.
\newline
(B) One dollar can buy
4
25
\frac{4}{25}
25
4
of a pint of paint.
\newline
(C) The art studio started with
4
25
\frac{4}{25}
25
4
of a pint of paint.
\newline
(D) The art studio can purchase at most
4
25
\frac{4}{25}
25
4
of a pint of paint.
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There are
4
4
4
squares that are shaded on grid. This represents
20
%
20\%
20%
of the total squares that are jn the grid. How many squares are there on the grid
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Camacho is buying a monster truck. The price of the truck is
\newline
x
x
x
dollars, and he also has to pay a
\newline
13
%
13\%
13%
monster truck tax.
\newline
Which of the following expressions could represent how much Camacho pays in total for the truck?
\newline
Choose
2
2
2
answers:
\newline
A
\newline
(
1
+
0.13
)
x
(1+0.13)x
(
1
+
0.13
)
x
\newline
B
\newline
13
100
x
\frac{13}{100}x
100
13
x
\newline
C
\newline
13
x
13x
13
x
\newline
D
\newline
1.13
x
1.13x
1.13
x
\newline
E
\newline
13
x
+
x
13x+x
13
x
+
x
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1
2
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