The cheerleaders from Danville High School are doing a giftwrapping fundraiser at a clothing store. Yesterday, they wrapped 15 small clothing boxes and 36 large clothing boxes, using a total of 492 feet of wrapping paper. The day before, they wrapped 39 small clothing boxes and 17 large clothing boxes, using a total of 360 feet of gift wrap. How much paper does it take to wrap each size of box?
Let's assume that the amount of paper required to wrap a small clothing box is s feet, and the amount of paper required to wrap a large clothing box is l feet.
From the first day of wrapping, we know that:
15s + 36l = 492 (1)
From the second day of wrapping, we know that:
39s + 17l = 360 (2)
To solve this system of equations, we can use the method of substitution.
From equation (2), we can isolate s:
39s = 360 - 17l
s = (360 - 17l)/39
Now we substitute this expression for s in equation (1):
15((360 - 17l)/39) + 36l = 492
Multiplying through by 39 to clear fractions:
15(360 - 17l) + 36(39l) = 492(39)
5400 - 255l + 1404l = 19218
5400 + 1149l = 19218
1149l = 13618
l = 13618/1149
l is approximately 11.8 feet.
Now we substitute this value for l in equation (2):
39s + 17(11.8) = 360
39s + 200.6 = 360
39s = 159.4
s is approximately 4.1 feet.
Therefore, it takes approximately 4.1 feet of paper to wrap each small clothing box, and approximately 11.8 feet of paper to wrap each large clothing box.