Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. $\newline$ The cheerleaders from Hampton High School are doing a giftwrapping fundraiser at a clothing store. Yesterday, they wrapped $40$ small clothing boxes and $20$ large clothing boxes, using a total of $400$ feet of wrapping paper. The day before, they wrapped $40$ small clothing boxes and $35$ large clothing boxes, using a total of $580$ feet of gift wrap. How much paper does it take to wrap each size of box? $\newline$ Each small box uses $\_$ feet of paper and each large one uses $\_$ feet.

View step-by-step help

View step-by-step help

Solve a system of equations using elimination: word problems

Full solution

Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

The cheerleaders from Hampton High School are doing a giftwrapping fundraiser at a clothing store. Yesterday, they wrapped

40

small clothing boxes and

20

large clothing boxes, using a total of

400

feet of wrapping paper. The day before, they wrapped

40

small clothing boxes and

35

large clothing boxes, using a total of

580

feet of gift wrap. How much paper does it take to wrap each size of box?

\newline

Each small box uses

\_

feet of paper and each large one uses

\_

feet.

Define Variables and Equations: Step $1$ : Define the variables and set up the equations based on the given information. $\newline$ Let $x$ be the amount of paper needed for each small box, and $y$ be the amount for each large box. $\newline$ From the first day: $40$ small boxes and $20$ large boxes used $400$ feet of paper. $\newline$ Equation: $40x + 20y = 400$ $\newline$ From the previous day: $40$ small boxes and $35$ large boxes used $580$ feet of paper. $\newline$ Equation: $40x + 35y = 580$
Simplify Equations: Step $2$ : Simplify both equations to make the numbers smaller and easier to work with. $\newline$ Divide the first equation by $20$ : $2x + y = 20$ $\newline$ Divide the second equation by $5$ : $8x + 7y = 116$
Use Elimination Method: Step $3$ : Use elimination to solve for one variable. We'll eliminate $y$ by making the coefficients of $y$ equal in both equations. $\newline$ Multiply the first simplified equation by $7$ : $14x + 7y = 140$ $\newline$ Now subtract this new equation from the second simplified equation: $8x + 7y = 116$ $\newline$ $(8x + 7y) - (14x + 7y) = 116 - 140$ $\newline$ $-6x = -24$
Solve for x: Step $4$ : Solve for x. $\newline$ Divide both sides by $-6$ : $x = 4$
Substitute to Find y: Step $5$ : Substitute $x = 4$ back into one of the simplified equations to find $y$ . Using $2x + y = 20$ : $2(4) + y = 20$ $8 + y = 20$ $y = 12$

More problems from Solve a system of equations using elimination: word problems

Question

Solve using elimination.

\newline

x + 6y = -15

\newline

-2x + 6y = 12

\newline

(\_,\_)

Posted 2 months ago

Question

(1,1)

a solution to this system of equations?

\newline

8x + y = 9

\newline

6x + 12y = 18

\newline

\newline

\newline

Posted 1 month ago

Question

How many solutions does the system of equations below have?

\newline

7

\newline

7

\newline

\newline

\text{[A]no solution}

\newline

\text{[B]one solution}

\newline

\text{[C]infinitely many solutions}

Posted 1 month ago

Question

Which describes the system of equations below?

\newline

y = \frac{1}{7}x - 10

\newline

y = \frac{1}{7}x - 10

\newline

\newline

\text{[A]consistent and independent}

\newline

\text{[B]consistent and dependent}

\newline

\text{[C]inconsistent}

Posted 1 month ago

Question

Solve using substitution.

\newline

y = -5

\newline

-4x + 3y = 17

\newline

Posted 1 month ago

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

\newline

Last Wednesday, two friends met up after school to read the book they were both assigned in Literature class. Bryan can read

2

pages per minute, and he had already read

98

pages. Jayla, who has a reading speed of

3

pages per minute, had read

48

pages. Eventually they had read the same number of pages. How long did that take? How many pages had each of them read?

\newline

\_\_\_\_

minutes, Bryan and Jayla had each read

\_\_\_\_

Posted 1 month ago

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

At the Castroville Ice Cream Parlor, one group of friends ordered

1

small serving of ice cream and

3

large servings of ice cream for

20

. Another group of friends ordered

1

small serving of ice cream and

4

large servings of ice cream for

26

. How much does the ice cream cost?

\newline

The ice cream costs `\$`_____ for a small serving and `\$`_____ for a large serving.

Posted 1 month ago

Question

\newline

y = -1

\newline

-2x - 4y = 8

\newline

(_____ , _____)

Posted 1 month ago

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

\newline

There are two mystery numbers. The sum of

3

times the first number and

3

times the second number is

-18

2

times the first number and

3

times the second number is

-13

. What are the two numbers?

\newline

The first number is ______ , and the second number is ______.

Posted 1 month ago

Question

A teacher purchased

300

colored pencils for an upcoming project. The pencils she ordered come in packs of

20

30

14

packs in all. Write a system of equations to find the number of

20

(x)

30

(y)

the art teacher ordered.

Posted 2 months ago