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
[tex]95(x+y=20)\\95x+95y=1900\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 2 from Eqn 3
[tex](95x+95y)-(95x+75y)=1900-1800\\95x+95y-95x-75y=100\\20y=100[/tex]
Dividing both sides by 20
[tex]\frac{20y}{20}=\frac{100}{20}\\y=5[/tex]
Putting y=5 in Eqn 1
[tex]x+5=20\\x=20-5\\x=15[/tex]
Mechanic A worked for 15 hours and mechanic B worked for 5 hours.
Keywords: linear equation, elimination method
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