Tim spent half of his allowance

Question

Tim spent half of his allowance going to the movies. He washed the family car and earned 8 dollars. What is his weekly allowance if he ended with 11 dollars?

Answer 1

he spent half his allowance going to the movies

then he earned $8 and had $11 left

x/2 + 8 = 11

x/2 = 11-8 = 3

x = 2(3) = $6 = his allowance

Answer 2

The amount of money Tim has left is equal to what he started with, takeaway what he spent, plus what he earned.

Let x = amount of his allowance (this is what is started with)

An expression for what is spent is 1/2 of that [ (1/2) x]

If M is the money he has left:

M = x - (1/2)x + 8. Since we know how much he has left (M = 11) the equation that models the situation is:

11 = x - (1/2)x + 8

11 = (1/2)x + 8

3 = (1/2)x

x = 6

When you reach this point in solving the equation:

11 = (1/2)x + 8, if you prefer to not work with fractions, multiply every term by 2:

22 = x + 16

x = 6

Check:

Tim started with $6, spent half of that ($3), so has $3 left. Then he earned $8, ending with 3+8 = $11.