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

Answer:

$128

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= $x- \frac{x}{2}$

Taking LCD as 2

⇒ Remaining earning= $\frac{2x-x}{2} = \frac{x}{2}$

Hence, remaining salary giving half earning to his mother is $\frac{x}{2}$

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

∴ Amount spent on shirt= $\frac{x}{2} \times \frac{1}{2} = \frac{x}{4}$

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

⇒ Amount left after spending on shirt= $\frac{x}{2} - \frac{x}{4}$

taking LCD as 4

⇒ Amount left after spending on shirt= $\frac{2x-x}{4} = \frac{x}{4}$

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

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

⇒$\frac{x}{4} = 32$

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

⇒ $\frac{x}{4} = 32$

Multiplying both side by 4.

⇒$x= 32\times 4$

∴ $x= \ 128$

Hence, Nghiep´s weekly earning is $128.