Tom had some money, he spent $33 on books and 3/5 of the remainder on toys. After that, he had 1/4 as much money as he had at first. How much money did Tom have left?
+37146 x = starter money
(x -33 ) 2/5 = amount after his spree
this equals 1/4 x
(x-33)(2/5) = 1/4 x
2/5 x - 66/5 = 1/4 x
8/20 x - 5/20 x = 66/5
x = 66/5 * 20/3 = 88 dollars originally 1/4 of which = 22 dollars left
+876 Tom had some money, he spent $33 on books and 3/5 of the remainder on toys. After that, he had 1/4 as much money as he had at first. How much money did Tom have left?
Let $n$ be the initial temperature
We have $n - 33 - \frac{3}{5}(n-33) = \frac{1}{4}n$
Simplifying the LHS: $\frac{2}{5}(n-33) = \frac{1}{4}n.$
Multiplying both sides by $5 \cdot 4 = 20$: $8(n-33) = 5n.$
Divide both sides by $8$: $n-33=\frac{5}{8}n.$
Subtract both sides by $\frac{5}{8}n$: $\frac{3}{8}n-33=0.$
Add both sides by $33$: $\frac{3}{8}n = 33.$
Multiply both sides by $\frac{8}{3}$: $n = \frac{8}{3} \cdot 33 = 8 \cdot 11 = 88.$
$\frac{1}{4} \cdot 88 = \boxed{22 \text{dollars}.}$
