Expert: Josh - 2/19/2008

Question
Doris spent 2/3 of her savings on a used car, and she spent 1/4 of her remaining savings on vintage fuzzy dice. If the dice cost her $250, how much did her original savings total?
I don't really get this problem, but i wan to. can you help me?

Answer
No problem Jason. In algebra problems, whenever there is an unknown quantity that we need to find, we give it a symbol. For example, we can call it "X" or something.

The thing unknown to us (what we need to work out) is Doris' savings. Let us call this X. Everything else in this problem can be expressed as a fraction of X.

The amount she spent on the used car represents two third of her total saving. Accordingly, the first cost component C1=(2/3)*X. The amount left over is clearly X-(2/3)*X, or (1/3)*X.

The money spent on vintage dice represents one quarter of her remaining savings. This amounts to 1/4 of "X-(2/3)*X". So, we can write C2=(1/4)*(1/3)*X=(1/12)*X for the second cost component.

We were told she spent C2 on the dice which cost her $250. This implies that (X/12)=250. Multiplying both sides by 12 gives X=12*250=2000.

She initially had $2000.