SOLUTION: 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? a) 43

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Question 261685: 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?
a) 43 b) 56 c) 21 d) 42 e) 65

Answer by Edwin McCravy(20062) About Me  (Show Source):
You can put this solution on YOUR website!
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.

system%2824+%3C+h+%3C+72%2C%0D%0Ah+=+7p%2C%0D%0Ah+=+6q%2B2%29

    24%3Ch%3C72 given
    24%3C7p%3C72 substituting 7p for h
    3%263%2F7%3Cp%3C10%262%2F7 dividing through by 7
1)  4%3C=p%3C=10 since p is an integer

7p=6q%2B2 since both = h

6p%2Bp=6q%2B2 writing 7p as 6p+p

p%2Bp%2F6=q%2B2%2F6 dividing through by 6

p%2F6-2%2F6=q-p isolating fractions

%28p-2%29%2F6=q-p combining fractions

The right side is an integer so the left side is too,
say k

%28p-2%29%2F6=k

p-2=6k multiplying through by 6

p=6k%2B2 solving for p

4%3C=p%3C=10 statement 1) above

4%3C=6k%2B2%3C=10 substituting 6k+2 for p

2%3C=6k%3C=8

1%3C=3k%3C=4

1%2F3%3C=k%3C=4%2F3

1%2F3%3C=k%3C=1%261%2F3

1%3C=k%3C=1 since k is an integer

k=1 

p=6k%2B2

p=6%281%29%2B2

p=8

h=7p

h=7%288%29

h=56

56 is a multiple of 7 and 2 more than 54,
which is a multiple of 6.

Answer 56 inches.

Edwin