The cheerleaders from Campo high school are doing a gift wrapping fundraiser at a clothing store. Yesterday, they wrapped 36 small clothing boxes and 25 large clothing boxes, using a total of 588 feet of wrapping paper. The day before, they wrap 27 small clothing boxes and 29 large clothing boxes, using a total of 564 feet of gift wrap. How much paper does it take to wrap each size of box?

Yesterday, they wrapped 36 small clothing boxes and 25 large clothing boxes, using a total of 588 feet of wrapping paper
The day before, they wrap 27 small clothing boxes and 29 large clothing boxes, using a total of 564 feet of gift wrap

We need to find how much paper it takes to wrap each size of box

Assume that they need x feet to wrap a small box and y feet to wrap a large box

∵ The small box is wrapped by x feet

∵ The large box is wrapped by y feet

∵ They wrapped 36 small clothing boxes and 25 large clothing

boxes, using a total of 588 feet

∴ 36x + 25y = 588 ⇒ (1)

∵ They wrapped 27 small clothing boxes and 29 large clothing

boxes, using a total of 564 feet

∴ 27x + 29y = 564 ⇒(2)

Now we have a system of equation to solve it

Multiply equation (1) by -3 and equation (2) by 4 to eliminate x

∵ -108x - 75y = -1764 ⇒ (3)

∵ 108x + 116y = 2256 ⇒ (4)

- Add equations (3) and (4)

∴ 41y = 492

- Divide both sides by 41

∴ y = 12

- Substitute the value of y in equation (1) or (2)

∵ 27x + 29(12) = 564

∴ 27x + 348 = 564

- Subtract 348 from both sides

∴ 27x = 216

- Divide both sides by 27

∴ x = 8

It takes 8 feet to wrap the small box and 12 feet to wrap the large box

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

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