Percentage word problem

Question

Joe spent 25% of his money on a sports drink. He spent 25% of the remaining money on trail mix. He had $9 left. How much money did he start out with?

Answer 1

Let the amount of money that Joe started with be "X".

 

After he bought the sports drink, he had X - (1/4)X=(3X)/4 left. Call this amount "Y" for the moment.

 

After he bought the trail mix, he had Y - (1/4)Y=(3Y)/4 left. But we also know that this was also equal to a whopping nine dollars.  So

 

(3Y)/4 = 9

 

But we can also substitute Y=(3X)/4 into this expression:

(3(3X)/4)/4) = (9X)/16 = 9

 

Solving for X, we find X=16.

 

Now check this answer. If Joe started with $16 and spent 25%, this would mean spending $4, leaving him with $12. Spending 25% of the $12 would mean dropping $3 on trail mix, leaving him with the $9 he's supposed to have for his date tonight!