Joel had $80 less than Hazel. Hazel spent $128 on a vacuum cleaner. As result, Joel had 4 times as much money as Hazel. How much money did both of them have altogether at first?
Well, let's break it down. If Hazel spent $128 on a vacuum cleaner and Joel had 4 times as much money left, that means Joel had $128 * 4 = $512 left.
We also know that Joel had $80 less than Hazel to start with, which means Hazel had $512 + $80 = $592 to begin with.
So, if we add up the initial amounts of money they had, the total amount would be $592 + $512 = $1,104.
Therefore, at first, Joel and Hazel had a grand total of $1,104. That's a lot of cash to clown around with!
Let's assume Joel initially had x dollars. Since Joel had $80 less than Hazel, Hazel initially had x + $80.
After Hazel spent $128 on a vacuum cleaner, Joel had 4 times as much money as Hazel. This means that Joel had 4 * ($128) = $512.
Since Joel initially had x dollars, we can set up the equation: x = $512.
Let's solve for x:
x = $512
Now, since Hazel initially had x + $80 dollars, Hazel had ($512 + $80) = $592.
To find the total amount of money they had altogether at first, we add Joel's initial amount and Hazel's initial amount:
Total = x + (x + $80)
Total = $512 + ($512 + $80)
Total = $512 + $592
Total = $1104
So, they had a total of $1104 altogether at first.