max said:

Lana had a fixed budget for a party. She spent 1/3 of the budget on decorations. Of the money that remains, she spent 3/4 on refreshments and the rest on door prizes for the group. If she spent $60 on door prizes, what was her budget?

I let buget = x

So decorations = (1/3)x

refreshments = 3/4(1/3(x))

door prizes = 60 which is 1/4(1/3(x))

I get budget = 720

Is that right?

Not exactly. But you're close!

If she spends 1/3 of the budgeted amount x for decorations, then she has 2/3 of the budgeted amount left! 1 - (1/3) = 2/3. If she spends (1/3)x on decorations, she will have (2/3)x remaining for other expenses.

And she spends (3/4) of this remaining amount on refreshments, so 1 - (3/4), or 1/4 of this amount will be left for door prizes. (1/4)*(2/3)x is the amount she has for door prizes.

And we know she has $60 for door prizes....

(1/4)(2/3)x = 60

(1/6)x = 60

x = 360

Now check....does this fit the conditions of the problem?