Question

(1) Ria is paid at the rate of $13.50 per hour. During a certain week she worked 40 hours. How much did she earn that week? (1 mark) (i) Ria worked 4 weeks in the month of August and her gross earnings was $2 463.75. Her regular week comprised 40 hours and overtime was paid at 1 1/2 times the hourly rate. Show that Ria worked 15 hours overtime in August. (2 marks) (iii) In August, 20% of Ria's gross earnings was deducted as tax. How much money does she have left after the deduction? (2 marks) (iv) Ria invested $219 of her earnings for 3 years at a rate of 4.5% per annum simple interest. How much interest does she receive after 3 years? (2 marks)​

Answer 1

The amount earned by Ria is given by the hourly rate less the amount

that she pays as tax.

Responses:

(i) $540

$(ii) \hspace{0.15 cm} The \ number \ of \ hours \ worked, \ x = \dfrac{303.75 }{13.5 \times 1\frac{1}{2}} = 15$

(iii) $1,971

(iv) $29.565

Which methods can be used to calculate the amount earned as salary?

(1) The rate Ria is paid per hour = $13.5

The number of hours Ria worked during the week = 40 hours

• The amount Ria earned = $13.50/hr × 40 hr. = $540

(2) The gross earnings in August = $2,463.75

The number of hours in a regular week = 40 hours

The over time rate = $\mathbf{1\frac{1}{2}}$ × Hourly rate

Let x represent the number of hours worked overtime

Therefore;

$13.5 × 40 × 4 + x ×  $1\frac{1}{2}$ × $13.5 = $2,463.75

$2,463.75 - $2,160 = $303.75 = x × $\mathbf{1\frac{1}{2}}$ × $13.5

$x = \dfrac{303.75 }{13.5 \times 1\frac{1}{2}} = \mathbf{15}$

• The number of hours worked overtime, x = 15 hours

(iii) Given that 20% was deducted as tax, the percentage of her salary left is 100% - 20% = 80% = 0.8

Which gives;

• Salary left in August = 0.8 × $2,463.75 = $1,971

(iv) The interest rate, R = 4.5% = 0.045

The amount invested, P = $219

Duration of the investment, T = 3 years

The interest after 3 years is therefore;

I = P·R·T

• Interest, I = $219 × 0.045 × 3 years = $29.565

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