Question

Cindy is deciding between a striped red-and-purple lunch box and a polka-dotted blue lunch box to buy for school. Each lunch box is shaped like a rectangular prism with a volume of 300 cubic inches. The red-and-purple lunch box is 7.5 inches wide and 4 inches tall. The blue lunch box is 8 inches wide and 3 inches tall.

How much longer is the blue lunch box than the red-and-purple lunch box?

Answer 1

Answer: 2.5 inches

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Step-by-step explanation:

x = length of the red and purple lunch box

y = length of the blue lunch box

volume = length*width*height

The volume expression for the red and purple lunch box is x*7.5*4 = 30x

Set this equal to the stated volume 300 cubic inches, and solve for x.

30x = 300

x = 300/30

x = 10

The red and purple lunch box has length of 10 inches.

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The blue lunch box has volume of

length*width*height = y*8*3 = 24y

Set this equal to 300 and solve for y

24y = 300

y = 300/24

y = 12.5

The blue lunch box has length of 12.5 inches

Therefore the blue lunch box is longer and is longer by 12.5-10 = 2.5 inches.