Question

-The side lengths of the middle-sized cube’s edges are 2 inches longer than those of the smallest cube.

- The side lengths of the largest cube’s edges are 2 inches longer than those of the middle-sized cube.
-The sum of one side length of each of the three cubes equals y.
- The volume of all three cubes combined is 24y. (Recall that Volume = length × width × height). three cubes of different colors and sizes in a stack
: Write a system of equations based on the given information.

Answer 1

The systems of equations is y=3x+6y

Answer 2

Assume that the side length of the smallest cube is x in

Part (a): getting the sides
We are given that the side length of the middle-sized cube's edge is 2 in longer than that of the smallest cube
This means that:
side length of middle cube = side length of smallest cube + 2
side length of middle cube = x + 2 in

We are given that the side length of the largest cube is 2 in longer than that of the middle-sized cube
This means that:
side length of largest cube = side length of middle cube + 2
side length of largest cube = x + 2 + 2
side length of largest cube = x + 4 in

Part (b): getting the system of equations
We are given that the sum of one side of each of the three cubes is y.
This means that:
y = side of smallest cube + side of medium cube + side of largest cube
y = x + x + 2 + x + 4
y = 3x + 6 .......> equation I

volume of smallest cube = length * width * height
volume of smallest cube = x*x*x = x³ in³
volume of middle cube = length * width * height
volume of middle cube = (x+2)(x+2)(x+2) = (x+2)³ in³
volume of largest cube = length * width * height
volume of largest cube = (x+4)(x+4)(x+4) = (x+4)³ in³
Sum of three volumes = 24y
This means that:
24y = x³ + (x+2)³ + (x+4)³ ........> equation II

Hope this helps :)