Mr. Ramos gave 3/5 of his lottery winnings to charity and spent ¼ of the remainder.  If he has $150 left, how much money did he have at first?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

Mr. Ramos gave 3/5 of his lottery winnings to charity and spent 1/4 of the remainder. 

Let the amount he had initially be X. When he gives away 3/5 of the amount he is left with `X*(1 - 3/5) = (2*X)/5` . He spends 1/4 of the remaining, the amount with him now is `((2*X)/5)*(1 - 1/4)` = `((2*X)/5)*(3/4) = (3*X)/10`

`(3*X)/10 = 150`

=> X = 500

Mr. Ramos initially had $500

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

Mr. Ramos gave 3/5 of his lottery winnings to charity and spent 1/4 of the remainder.  The amount left with him after this is $150.

Starting with $150, this is 3/4 of another number, taking into account that he spent 1/4th of that amount. This gives the amount as `150/(3/4) = 4*150/3` = 200.

The $200 is 2/5 of the amount he won as 3/5 was given away as charity. This gives the amount he won as `200/(2/5) = 200*5/2` = 500.

Ramos won $500.

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