Question

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.

Answer 1

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

Answer 2

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.

Answer 3

x + (x + 17) = 45

Answer 4

Let a represent the new tire and n represent the old tire.

n + a = $45

n + (n + 17) = $45 (since one tire costs $17 more than the other)

That may also be written as, 2n + 17 = 45.

In that situation, you subtract 17 from 17 and then 17 from 45.

The result is n=14.

Now, it is figured out that the old tire was $14.

If the new tire is $17 more, you add 14 and 17.

14+17=31

The new tire costs $31 and the old tire costs $14.