Devi spent (2/3) of her monthly allowance on food and (5/6) of the remaining amount on stationery. She spent $35 more on food than on stationery. How much as Devi's monthly allowance?
My work:
Number of allowance = A Number spent on Food = F Number spent on Stationary = S
[1] We know Devi spent (2/3) of her allowance. so 1 - (2/3) = 1/3A (so 1/3 of her allowance is left)
[2] We know she spent (5/6) of her remaining allowance. So (1/3) * (5/6) = 5/18A (I'm guessing 5/18A is the amount of allowance left?)
[3] She spent $35 more on food than on stationery. So, (F + 35) + S = A
[4] We plug it into this forum (F + 35) + S = A (1/3A + 35) + 5/18A = A
Answer: A = 90
If this is correct, is there a better way for me to do this?
You got the correct answer, but you could clean up your reasoning as follows:
Define A to be total allowance, F to be allowance spent on food, and S to be allowance spent on stationary.
Since she spent 35 more on stationary than on food, then $35+S=F$. Also, $F=(2/3)A$ and $S=(5/6)(A-F)=(5/6)(A-(2/3)A)=(5/6)(1/3)A=(5/18)A$
Using substitution, $35+(5/18)A=(2/3)A$ so $A=90$.