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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?

 May 11, 2021
 #1
avatar+34306 
+1

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

 May 11, 2021
 #2
avatar+775 
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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 $\frac{8}{3}$: $n = \frac{8}{3} \cdot 33 = 8 \cdot 11 = 88.$

$\frac{1}{4} \cdot 88 = \boxed{22 \text{dollars}.}$

 May 11, 2021

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