v1 Financial Maths, STD2 F1 2024 HSC 23

Dave works a 40-hour week and is paid at an hourly rate of $20. Any overtime hours worked are paid at time-and-a-half.

Last week, Dave worked the regular 40 hours and some overtime hours. In that week, Dave earned $1250.

How many hours of overtime did Dave work last week? (3 marks)

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$\text{15 hours of overtime}$

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$\text {Let X = overtime hours}$

	$\text{Total pay}$	$=(40 \times 20)+\Big(X \times \dfrac{3}{2}\times 20\Big) $
	$1250$	$=800+\dfrac{60}{2}X$
	$\dfrac{60}{2}X$	$=450$
	$X$	$=\dfrac{450\times 2}{60}$
		$=15 \text{ hours of overtime}$

	\(\text{Total pay}\)	\(=(40 \times 20)+\Big(X \times \dfrac{3}{2}\times 20\Big) \)
	\(1250\)	\(=800+\dfrac{60}{2}X\)
	\(\dfrac{60}{2}X\)	\(=450\)
	\(X\)	\(=\dfrac{450\times 2}{60}\)
		\(=15 \text{ hours of overtime}\)