Question

Huw is paid a weekly wage. Every week he:

saves 1/5

of his wage,

spends 70% of the money he has left on his living expenses,

spends all that remains on his social life.

One week, Huw saves £40.
How much does Huw spend on his social life?

Answer 1

Step-by-step explanation:

Let the wage be £ w

Condition 1. He saves 1/5 of his wage.

Then he saves £ w/5

So left amount

= £ (w - w/5)

= £ 4w/5

Condition 2. He spends 70% of the money left on his living expenses.

Then he spends £ 4w/5 × 70/100

= £ 14w/25

Thus remaining amount

= £ (4w/5 - 14w/25)

= £ 6w/25

Condition 3. He spends the remaining amount on his social life.

Then £ 6w/25 is the amount he spends on his social life.

Condition 4. He saves £ 40 in a week.

Then from Condition 1, we can write

w/5 = 40 ( numerically)

⇒ w = 200

From Condition 3, we can get the amount spend on his social life

= £ 6 × 200 / 25

= £ 48

Answer:

He spends £48 on his social life.