Question

QUESTION 10.2 Two mechanics worked on a car. The first mechanic charged $ 95 per hour, and the second mechanic charged $ 75 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $ 1800 . How long did each mechanic work?

Answer 1

Mechanic A worked for 15 hours and mechanic B worked for 5 hours.

Step-by-step explanation:

Given,

Per hour charges of mechanic A = $95

Per hour charges of mechanic B = $75

Total hours worked = 20

Total amount charged = $1800

Let,

x represent the number of hours of mechanic A

y represent the number of hours of mechanic B

According to given statement;

x+y=20          Eqn 1

95x+75y=1800   Eqn 2

Multiplying Eqn 1 by 95

$95(x+y=20)\\95x+95y=1900\ \ \ Eqn\ 3$

Subtracting Eqn 2 from Eqn 3

$(95x+95y)-(95x+75y)=1900-1800\\95x+95y-95x-75y=100\\20y=100$

Dividing both sides by 20

$\frac{20y}{20}=\frac{100}{20}\\y=5$

Putting y=5 in Eqn 1

$x+5=20\\x=20-5\\x=15$

Mechanic A worked for 15 hours and mechanic B worked for 5 hours.

Keywords: linear equation, elimination method

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