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?
The easy way is to try out the 5 choices. It can't be a) because 43 is not
a multiple of 7. It can't be c) because 21 is 2 more than 19 which is not
a multiple of 6. It can't be d) because 42 is 2 more than 40, which is not
a multiple of 6. It can't be e) because 65 is not a multiple of 7. So
that leaves only b).
However that's no fun. I am going to pretend this wasn't a multiple
choice question and work it out without using any of those choices.
given
substituting 7p for h
dividing through by 7
1) since p is an integer
since both = h
writing 7p as 6p+p
dividing through by 6
isolating fractions
combining fractions
The right side is an integer so the left side is too,
say k
multiplying through by 6
solving for p
statement 1) above
substituting 6k+2 for p
since k is an integer
56 is a multiple of 7 and 2 more than 54,
which is a multiple of 6.
Answer 56 inches.
Edwin