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+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
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.
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.
To find the cost of the new tire, you can use algebra. Let's call the cost of the used tire "x". Since the new tire costs $17 more than the used tire, its cost can be represented as "x + 17".
The total cost of both tires is $45. So we can create an equation based on this information:
x + (x + 17) = 45
Now we can solve this equation to find the value of x, which represents the cost of the used tire:
2x + 17 = 45 (Combine like terms)
2x = 45 - 17 (Subtract 17 from both sides)
2x = 28 (Simplify)
x = 14 (Divide both sides by 2)
Therefore, the used tire costs $14.
To find the cost of the new tire, we can substitute the value of x into the equation:
x + 17 = 14 + 17 = 31
So, the cost of the new tire is $31.
In summary, you can use algebra to solve the problem by creating an equation and then solving it to find the value of the variable representing the unknown cost.