It takes 8 feet to wrap the small box and 12 feet to wrap the large box
Step-by-step explanation:
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
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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