Math
posted by Miranda .
Casey paid $45 for one new tire and one used tyre for his bicycle. The new tire costs $17 more than the used tire. How much did the new tire cost?
I have worked out the answer in my head, ($31) but is there a particular formula I can use or follow.

Let's new = x, old = y
x+y = 45
x= y+17
y+17+y = 45
2y+17 = 45
2y+1717=45 17
2y = 28
2y/2 = 28/2
y = 14
x = y+17
x = 14+17
x = 31
So new tire cost $ 31 and used tire cost $ 14 
Shortcut for sum/difference problems:
Whenever the sum and difference of two numbers are both given, the bigger number is (sum+difference)/2, and the smaller number is (sumdifference)/2.
(45+17)/2=31
(4517)/2=14
Most of the time these problems can be solved without pen and paper. 
x + (x + 17) = 45