-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.
Accepted Solution
A:
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