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
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.
4 answers
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.
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.
x + (x + 17) = 45
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.
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.