Question

One number is 4 more than another. the difference between their squares is 64. what are the numbers

Answer 1

We have to set up 2 different equations if we are to solve for 2 unknowns.  The first equation is x = y + 4.  One number (x) is (=) 4 more than another (y + 4).  Since we have determined that x is larger (cuz it's 4 more than y), when we set up their difference, we are going to subtract y from x cuz x is bigger.  The second equation then is $x^{2} - y^{2} =64$.  In our first equation we said that x = y + 4, so let's sub that value in for x in the second equation: $(y+4) ^{2} - y^{2} =64$.  Expand that binomial to get $y^{2} +8y+16- y^{2} =64$.  Of course the y squared terms cancel each other out leaving us with 8y + 16 = 64.  Solving for y we get that y = 6.  Subbing 6 in for y in our first equation, x = 6 + 4 tells us that x = 10. Yay!