Question

John works two jobs. As a security guard he earns $8.50 per hour. As a landscaper he earns $14 per hour. One week John worked a total of 60 hours and earned $691.50. How many hours did he work at each job?

Answer 1

John worked 27 hours as security guard and 33 hours as landscaper.

Step-by-step explanation:

Given,

Cost per hour as security guard = $8.50

Cost per hour as landscaper =$14

Total hours = 60

Total earned = $691.50

Let,

x be the number of hours worked as security guard.

y be the number of hours worked as landscaper.

According to given statement;

x+y=60    Eqn 1

8.50x+14y=691.50    Eqn 2

Multiplying Eqn 1 by 8.50

$8.50(x+y=60)\\8.50x+8.50y=510\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2

$(8.50x+14y)-(8.50x+8.50y)=691.50-510\\8.50x+14y-8.50x-8.50y=181.50\\5.5y=181.50$

Dividing both sides by 5.5

$\frac{5.5y}{5.5}=\frac{181.50}{5.5}\\y=33$

Putting y=33 in Eqn 1

$x+33=60\\x=60-33\\x=27$

John worked 27 hours as security guard and 33 hours as landscaper.

Keywords: linear equation, subtraction

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