Julia deposited 1/2 her paycheck in her savings account and 1/4of it in her checking account. She spent $22.76 of it on a T-shirt and then spent 1/4 of what was left of her paycheck on lunch. When she arrived home, she had $16.68 of her paycheck left. How much money did Julia receive in her paycheck?
To find out how much money Julia received in her paycheck, we need to work backwards from the amount she had left.
First, let's calculate the amount she had left after spending on lunch. We know Julia had $16.68 remaining, which represents 1/4 of what was left after buying the T-shirt. So, we can set up an equation:
1/4 * (what was left - $22.76) = $16.68
To simplify the equation, let's isolate the expression in the parentheses:
What was left - $22.76 = $16.68 * 4/1
Simplifying the right side:
What was left - $22.76 = $66.72
Next, let's calculate the amount Julia had before spending on lunch. Again, we can set up an equation:
(What was left - $22.76) + $66.72 = Julia's paycheck
To simplify the equation, let's combine like terms:
What was left + $66.72 - $22.76 = Julia's paycheck
What was left + $43.96 = Julia's paycheck
Now, let's plug in the value we know:
What was left + $43.96 = $88.00
Subtracting $43.96 from both sides:
What was left = $88.00 - $43.96
What was left = $44.04
So, Julia received $44.04 in her paycheck.
paycheck --- x
she saved (1/2)x + (1/4)x or (3/4)x
leaving her with (1/4)x
after spending $22.76 on t-shirt, leaves her with
(1/4)x - 22.76
(1/4)x - 22.76 = 16.68
(1/4)x = 39.44
x = 157.76