Question

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?

*Remember to show your work and triple check it to see if your answer is correct*

*Singapore Math*

Answer 1

Gary had $192.

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 =
`(1)/(3)(x - 48)`

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

`(x)/(2)=48+(1)/(3)(x - 48)`

`(x)/(2)=48+(x)/(3)-(48)/(3)`

`(x)/(2)=(x)/(3)+32`

`(x)/(2)-(x)/(3)=32`

`(3x-2x)/(6)=32`

`(x)/(6)=32`

x = 6×32

x = 192

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

Money spent on a pen =
`(144)/(3)` = $48

Money left = 144 - 48

= $96

This amount is half of the total money =
`(192)/(2)`

= $96

Answer 2

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

48 + 1/3 T -1/3*48= 1/2 T
48 - 16 =1/2 T- 1/3 T
32= 1/6 T
T= 6*32
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.