Question

3. Nghiep gave his mother half of his weekly earnings, and then spent half of what was left on a new shirt. He then had $32. What were his weekly earnings?

Answer 1

$128

Step-by-step explanation:

Given: Nghiep gave half of his weekly salary to his mother.

Spent remaining half on a new shirt.

Finally he is left with $32

Lets assume Nghiep´s weekly earning be "x".

As given, Nghiep gave his mother half of weekly earning.

∴ Remaining earning=
`x- (x)/(2)`

Taking LCD as 2

⇒ Remaining earning=
`(2x-x)/(2) = (x)/(2)`

Hence, remaining salary giving half earning to his mother is
`(x)/(2)`

Now, as given Nghiep spent half of what was left on a new shirt.

∴ Amount spent on shirt=
`(x)/(2) * (1)/(2) = (x)/(4)`

Next, finding the amount left with Nghiep after spending on shirt.

⇒ Amount left after spending on shirt=
`(x)/(2) - (x)/(4)`

taking LCD as 4

⇒ Amount left after spending on shirt=
`(2x-x)/(4) = (x)/(4)`

As given, Nghiep left with $32 after spending on shirt.

∴ We can form an equation for amount left with Nghiep after spending on shirt.

⇒
`(x)/(4) = 32`

Now, solving it to find the weekly earning of Nghiep.

⇒
`(x)/(4) = 32`

Multiplying both side by 4.

⇒
`x= 32* 4`

∴
`x= \$ 128`

Hence, Nghiep´s weekly earning is $128.