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Gary spent $48 on a watch. He spent 1/3 of the remainder on a pen if he still had 1/2 of his money left,how much money did he have at first?


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Singapore Math

Verified Answer :

loganwatson11

T= total
Money spent is: 
48+ 1/3 (T-48) = 1/2 T
One equation for one unknown, solve:

48 + 1/3 T -1/348= 1/2 T
48 - 16 =1/2 T- 1/3 T
32= 1/6 T
T= 632
T=192

192-48=144 money left after watch
1/3*144=48 third of leftover, spent on pen
144-48=96 left which is half of 192. 

Answer:

Gary had $192.

Step-by-step explanation:

Let Gray has the money = $x

Gray spent on a watch = $48

Remainder money = $(x - 48)

He spent one third of the remainder on a pen.

Money spent on a pen = \(\frac{1}{3}(x - 48)\)

This remainder money is the half of x then the total money spent

\(\frac{x}{2}=48+\frac{1}{3}(x - 48)\)

\(\frac{x}{2}=48+\frac{x}{3}-\frac{48}{3}\)

\(\frac{x}{2}=\frac{x}{3}+32\)

\(\frac{x}{2}-\frac{x}{3}=32\)

\(\frac{3x-2x}{6}=32\)

\(\frac{x}{6}=32\)

x = 6×32

x = 192

Money left after spending on watch = 192 - 48 = $144

Money spent on a pen = @@MATH_TOKEN_7@@ = $48

Money left = 144 - 48

                 = $96

This amount is half of the total money = @@MATH_TOKEN_8@@

                                                               = $96

               

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