Final answer:
The shortest height at which two stacks of boxes, one with 12-inch boxes and the other with 18-inch boxes, will be the same height is 36 inches, as it is the least common multiple of the two measurements.
Step-by-step explanation:
The question involves finding the shortest height at which two stacks will be the same height, when the stacks are composed of boxes that are respectively 12 inches and 18 inches in size. This problem is a least common multiple (LCM) problem, where you want to find the smallest number that both 12 and 18 can divide into without leaving a remainder, because this will give you the height at which both stacks are equal.
To find the LCM of 12 and 18, you could list the multiples of each number until you find the smallest common one:
- 12: 12, 24, 36, 48, 60, ...
- 18: 18, 36, 54, 72, 90, ...
As we can see, the smallest number that appears in both lists is
36
. Hence, the two stacks would be the same height when they reach
36 inches
tall.
]