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Two mechanics worked on the car the first mechanic work for five hours in a sec mechanic work for 15 hours together the tires a total of 1850 what was the rate charge per hour about each mechanic if the sum of the two rates were $160 per hour

Answer :

MrRoyalgo

Answer:

Mechanic 1: $55 per hour

Mechanic 2: $105 per hour

Step-by-step explanation:

Given

Represent the rate of the first mechanic with x and the second with y.

So, we have:

[tex]x + y = 160[/tex]

The total earnings is: $1850, so we have:

[tex]5x + 15y = 1850[/tex]

Required

Determine the rate of each

The equations are:

[tex]x + y = 160[/tex] --- (1)

[tex]5x + 15y = 1850[/tex] --- (2)

Divide (2) through by 5

[tex]x + 3y = 370[/tex] --- (3)

Subtract (1) from (3)

[tex]x - x + 3y - y = 370 - 160[/tex]

[tex]2y = 210[/tex]

Divide through by 2

[tex]y = \frac{210}{2}[/tex]

[tex]y = 105[/tex]

Substitute 105 for y in (1)

[tex]x + y = 160[/tex]

Make x the subject

[tex]x = 160 - y[/tex]

Substitute 105 for y

[tex]x = 160 - 105[/tex]

[tex]x = 55[/tex]

Hence:

Mechanic 1: $55 per hour

Mechanic 2: $105 per hour

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