Expert: Scott A Wilson - 10/26/2011

Question
"I was given a=13; y=7; a-y=6. Using these make an equation that gives 87 as it's answer. Then use the same equation and make a=21; y=13 and a-y=8 giving the answer of 79. HELP PLEASE!"

Answer
If we take a=13, y=7. and a-y=6, and are suppose to get 87,
then it could be 87a/13 = 87.  If we put in a as 13, this can be seen to be true.

If we want integers, then if we had 1a, is would leave 87-13=76, and this is not divisible by 7.

Using 2 gives 87 - 2(13) = 87 - 26 = 61. amd that is not divisible by 7.

Using 3 gives 87 - 3(13) = 87 - 39 = 48, and that is not divisible by 7.

Using 4 givevs 87 - 4(13) = 87 - 52 = 35, and 35 is 5*7.
This makes the equation 4a + 5y = 87, for 4a = 52, 5y = 35, and 42 + 35 = 87.

If we wanted to, a-y = 6 could be used.  Note that 7a = 91, and 87 is 4 short.
Now y - a-y = 1, so 4 is 4y - 4(a-y).  Since it is suppose to be -4, take -4y + 4(a-y).
This makes it 87 = 7a - 4y + 4(a-y).  This is 7*13 - 4*7 + 4*6 = 91 - 28 + 24 = 91 - 7 = 84.

Needless to say, there are endless possibilities.


For a=21, y=13, and a-y-8, to get to 79,  we could use 2a, which is 42.
That would leave us with 79-42=37.  Note that if we used 1 for y, we would have 37-13=24.
Now 24=3*8, and a-y=8, so we would have 3(a-y).  This makes 2a + 1y + 3(a-y) = 42 + 13 + 24.
This is correct, for 42+13=55, and 55+24=79.