Answer:
56
Step-by-step explanation:
The difference between 6 and 7 is 1, so the difference between 2×6 = 12 and 2×7 = 14 will be 2×1 = 2.
The solutions to
6a +2 = 7b
for integers a and b will be of the form ...
a = 7n +2
b = 6n +2
Which makes ...
7b = 7(6n +2) = 42n +14
The value of n that gives a value of 7b in the range of 24 to 72 is n = 1.
For that value, the height in inches is ...
42×1 +14 = 56 . . . . inches
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Check
56 = 7×8, a multiple of 8
56 = 54 +2 = 6×9 +2. This is 2 more than a multiple of 6
