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8. Each box in a set of decorative storage boxes is a cube.
a) The sides of the smallest box are 30% of the length of the sides of the largest
box. The volume of the largest box is 7784 cubic inches more than the
volume of the smallest box. Define one or more variables, and write an
equation that represents the situation.
b) What are the lengths of the sides of the largest and smallest boxes?
c) Two of the other boxes have a total volume of 2457 cubic inches. The length
of the sides of the smaller of these boxes is 75% of those of the larger box.
Write and solve an equation to find the lengths of the sides of the boxes.

Answer :

MHANIFAGO

Answer:

  • 20 in and 6 in
  • 12 in and 9 in

Step-by-step explanation:

a) Let the side of the larger box be x, then the side of the smaller box is 0.3x.

Their volumes are:

  • x³ and
  • (0.3x)³ = 0.027x³

The difference in volumes:

  • x³ - 0.027x³ = 7784
  • 0.973x³ = 7784
  • x³ = 7784/0.973
  • x³ = 8000
  • x = ∛8000
  • x = 20

b) The sides are 20 in and 20*0.3 = 6 in

c) The other two boxes with sides x and 0.75x

Sum of the volumes:

  • x³ + (0.75x)³ = 2457
  • x³ + 0.421875x³ = 2457
  • 1.421875x³ = 2457
  • x³ = 2457/1.421875
  • x³ = 1728
  • x = ∛1728
  • x = 12

Sides of the boxes are 12 in and 12*0.75 = 9 in

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