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Solve system of equations: Complex word problems

\$48,000

salary per year. In order to qualify for an

85

\%

loan, his monthly PITI payment cannot be more than

28

\%

of his monthly salary. The annual taxes and insurance will be

\$2,352.60

. If the monthly principal and interest payment is

\$6.00

\$1,000

of loan amount, what is the most sales price he can afford?

David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is

15:1

. He currently has

40

grams of the spice blend, and he can go buy more if necessary. He wants to make

10

servings, where each serving has

75

grams of rice. Overall, David spends

4.50

dollars on rice.

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What is the price of rice per gram?

₹ 3,690

, whereas an almirah costs

₹ 12,810

more than the cost of the table. Find the total cost of both the table and aimirah.

The cost to produce

10

£ 2.40

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The cost to produce

8

£ 2.40

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Key rings are sold in boxes of

200

£ 60

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Bangles are sold in baxes of

400

£ 140

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How much more profit is made on a box of bangles than on a box of key rings?

For a particular delivery, a courier travels by bicycle at a speed of

v

miles per hour for a distance of

1

3

miles. After making the delivery, the courier travels the same distance back, but travels

2

miles per hour faster than on the way to the delivery. If the courier spent

0

2

hours travelling to and from the delivery, which of the following equations could be used to determine the speed of the bicycle on the way to the delivery?

Four items are served to everyone who eats at a breakfast buffet.

36

people ate on Monday,

45

64

50

on Thursday, and

55

on Friday. How many servings in total were served at the buffet from Monday to Friday?

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250

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600

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750

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1,000

You currently drive

240

miles per week in a car that gets

24

miles per gallon of gas. You are considering buying a new fuel-efficient car for

\$ 13,000

(after trade-in on your current car) that gets

40

miles per gallon. Insurance premiums for the new and old car are

\$ 720

\$ 500

per year, respectively. You anticipate spending

\$ 1050

per year on repairs for the old car and having no repairs on the new car. Assume gas costs

\$ 2.45

per gallon. Over a seven-year period, is it less expensive to keep your old car or buy the new car? By how much?

\$ 16.90

to place an advertisement in a local newspaper. The total cost is determined by a

\$ 4.50

set up cost and a

\$ 0.40

per word cost. How many words were in Rebecca's advertisement?

Question Completion Status:

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Moving to another question will save this response.

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24

25

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4

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24

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per gallon. Over a seven-year period, is it less expensive to keep your old car or buy the new car? By how much?

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\$3420.08

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\$3622.80

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\$3420.08

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\$3622.80

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Moving to another question will save this response.

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24

25

A given number is a multiple of

7

. It is between

30

60

. It is also a factor of

70

. What is the number?

4

. The total cost of a table and

6

\$ 668

0

\$ 18

. Find the cost of the table.

Catriona earns a salary of

\$87,210

and claims these deductions:

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Travel and entertainment expenses

\$650.25

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Depreciation of home computer

\$314.80

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Membership of a professional association

\$120.50

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a Calculate Catriona's taxable income.

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b Calculate Catriona's income tax payable.

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c What is the amount of Catriona's Medicare levy?

Systems by Substitution

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Clark spent a total of

\$ 46

on a pair of shoes and a new jacket. The shoes cost

\$ 8

more than the jacket. Write a system of equations to represent the situation. Then find the cost of each irem.

opposite directions. A line segment is a part of a line with two endpoints. A ray is a part of a line that has one endpoint and continues on forever in one direction. Label each figure with the correct term.

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\stackrel{\bullet}{G}

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2

. Angles can be classified by their measures. A right angle forms a square corner. An acute angle is open less than a right angle. An obtuse angle is open more than a righ angle but is open less than a straight angle. A straight angle forms a straight line. Identify each type of angle.

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3

. Use a geometric term to describe and name each figure.

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Be as specific as possible.

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The figure at the right is a

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Name the figure using the points that are labeled.

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4

. The figure at the right is an angle.

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Name the angle with the points from each ray and the shared

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endpoint of the rays. The shared endpoint is the center letter.

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5

. Use a geometric term to describe each figure. Be as specific as possible.

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15

1

Each big square below represents one whole. An array with

10

10

rows that represents

1

10

10

are shaded. An array with

10

10

rows that represents

1

10

10

are shaded. An array with

10

10

rows that represents

1

1

10

4

is shaded. An array with

10

10

rows that represents

1

1

10

4

is shaded. What percent is represented by the shaded area?

Fabiano wants to score at least

6.5

points in a major chess tournament. He scores

1

point for each game that he wins, and he scores

0.5

points for each game that ends in a draw. Which of the following inequalities represents the number of games Fabiano should win

(W)

(D)

to achieve his goal?

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1

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W+0.5D \leq 6.5

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0.5W+D \geq 6.5

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W+0.5D \geq 6.5

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0.5W+D \leq 6.5

b) Emma's limo service charges

\$ 50

\$ 2.10

per km. Sarah's limo service charges

\$ 42

\$ 2.20

per km. When do they charge the same amount?

16

-ounce bottle of Fresh Water is

\$ 1.76

20

-ounce bottle of Spring Water is

\$ 2.40

. Which statement about the unit prices is true?

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Spring Water has a lower unit price of

\$ 0.11

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Fresh Water has a lower unit price of

\$ 0.11 /

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Spring Water has a lower unit price of

\$ 0.12

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Fresh Water has a lower unit price of

\$ 0.12 /

My grandmother needs to find the best company to deliver a package. Company A charges a fee of

\$ 14

\$ 7

per pound. Company B charges a fee of

\$ 15

\$ 6

per pound. At what weight will the companies charge the same amount and what is the equivalent cost?

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y

7

x

4

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y

6

x

5

The sum of the first

6

terms of a geometric series is

15624

and the common ratio is

5

. What is the first term of the series?

Dorris is trying to decide between two laser printers. Both have similar features and warranties so price is the determining factor. Printer A costs

\$ 159

and printing costs are approximately

\$ 0.04

per page Printer B costs

\$ 194

. and printing costs are approximately

\$ 0.02

per page. How many pages need to be printed for the cost of the two printers to be the same?

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pages need to be printed for the cost of the two printers to be equal.

If the price of a

7

-pound bag of dried black beans is

\$9.80

, which of the following statements is true?

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1

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(A) The price of the dried black beans is

\$1.00

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(B) The price of the dried black beans is

\$1.40

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(C) The price of the dried black beans is

\$2.80

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(D) The price of the dried black beans is

\$68.60