SOLUTION: Okay....trying to help my sixth grade daughter here with this equation. If Paula spends 1/3 of her money on a meal then a 1/4 of what was left on gifts then a 1/5 of what was le

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Okay....trying to help my sixth grade daughter here with this equation. If Paula spends 1/3 of her money on a meal then a 1/4 of what was left on gifts then a 1/5 of what was le      Log On


   

Question 861727: Okay....trying to help my sixth grade daughter here with this equation.
If Paula spends 1/3 of her money on a meal then a 1/4 of what was left on gifts then a 1/5 of what was left at the museum. She is left with $32.40. What did she start with.
Kind regards
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Call what she started with, w, for "whole amount she started with". This is a number, but we do not know its value.

Try to form a step-wise process. First part,w-%281%2F3%29w. Simplify this NOW.
%282%2F3%29w is what she has.

Second part, %282%2F3%29w-%281%2F4%29%282%2F3%29w is what she has when spent the second part. Simplify this now. LCD is 12, seeing denominators as factors being 4 and 3.
%282%2F3%29w%284%2F4%29-%281%2F4%29%282%2F3%29w
%288%2F12%29w-%282%2F12%29w
%286%2F12%29w
%281%2F2%29w

Third part, spending one fifth of the current amount at the museum.
%281%2F2%29w-%281%2F5%29%281%2F2%29w, and LCD is 10.
%285%2F10%29w-%281%2F10%29w
%284%2F10%29w
%282%2F5%29w
-
Finally, we are told that this amount is $32.40; so we have
%282%2F5%29w=32.40

How do you undo multiplication by a fraction? Multiply by the reciprocal. Do this to BOTH sides of the equation! What happens to the left-side member? What happens to the right-side member?