# Math

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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.

• Math -

Let's new = x, old = y

x+y = 45

x= y+17

y+17+y = 45

2y+17 = 45

2y+17-17=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

• Math -

Short-cut 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 (sum-difference)/2.

(45+17)/2=31
(45-17)/2=14

Most of the time these problems can be solved without pen and paper.

• Math -

x + (x + 17) = 45

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