# Jose wins big on a scratch-off ticket. after paying 25% in taxes and paying off his car loan of $32,000, he has $ 22,000 left. what was the grand prize of the lottery before taxes were applied and before Jose paid off his car loan?

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Feb 8, 2018

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$72,000

#### Explanation:

Work backwards to solve this problem.

1) He has $22,000 left. Add the $32,000 he just spent for his car loan

22,000+32,000=54,000

So after he pays 25% in taxes, Jose has $54,000 before paying off his loan of $32,000.

2) Jose uses 25% of the total money received from the lottery ticket to pay taxes. 100%-25%=75%. We are working backwards, so the $54,000 we solved for in the last step would represent 75% of the money he won. From this, we can make a proportion:

Let x=the total amount of money Jose won

Explanation: 54,000 represents 75% of the total amount of money won, therefore, x represents 100% of the money.

3) Cross multiply

54,000•100=75x

5400000=75x

72000=x

Jose won $72,000 in total

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