# Math Help - Help Please: Fraction Word Problem

1. ## Help Please: Fraction Word Problem

This is the problem: Arnie spent 1/2 of his money at the movies, 1/3 of what was left on yogurt, and his last $4 on a gift. How much did Arnie spend? I've been able to figure out other ones similar to this problem, but for some reason I can't figure this one out. I'm not sure where to start. Any help would be greatly appreciated. Thank you. 2. Originally Posted by mary07 This is the problem: Arnie spent 1/2 of his money at the movies, 1/3 of what was left on yogurt, and his last$4 on a gift. How much did Arnie spend?

I've been able to figure out other ones similar to this problem, but for some reason I can't figure this one out. I'm not sure where to start.

Any help would be greatly appreciated. Thank you.
Let M be his total money.

$M=\frac{M}{2}+\frac{M}{6}+4$

Solve for M.

3. Hello, Mary!

We can talk our way through thiis one . . .

Arnie spent 1/2 of his money at the movies,
1/3 of what was left on yogurt,
and his last $4 on a gift. How much did Arnie spend? Let $M$ = original amount of money. He spent half of it the movies. .He spent $\frac{1}{2}M$ dollars. . . He had $\frac{1}{2}M$ dollars left. He spent a third of this on yogurt. .He spent: . $\frac{1}{3}\left(\frac{1}{2}M\right) \:=\:\frac{1}{6}M$ dollars. . . He had: . $\frac{1}{2}M - \frac{1}{6}M\:=\:\frac{1}{3}M$ dollars left. This is the$4 he spent on a gift: . $\frac{1}{3}M \;=\;4\quad\Rightarrow\quad M \:=\:12$

Therefore, Arnie spent \$12.

4. Whoops, my original solution was going with 1/3 of the original amount, not of what was left.

5. Thanks to both of you for your quick and detailed help. You made sense of the problem for me. Thanks so much!

Mary