Question

i am less than 6 feet tall but more than 2 feet tall. my height in inches is a multiple of 7 and is also 2 inches more than a multiple of 6. what is my height in inches

Answer 1

56

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