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Dalton is an apprentice electrician to Willard, who is a master electrician with his own business. Willard earns $22 per hour more than Dalton when working on-site on a job for a customer. Willard spent 6 hours working on wiring at Mrs. Kingbury's house on Saturday. Dalton worked with Willard for 3 of those hours. If the total labor cost for this time on Saturday for both Willard and Dalton was $492,then how much does each one of them earn per hour when working on-site on a job?

Let x= Dalton's hourly pay when working on-site on a job for a customer
Let y= Willard's hourly pay when working on-site on job for a customer
Select the 2 equations that can be used together to answer this question and select 2 viable answers based on the given constraints.

y= x+22 x-y=22
6x+3y=492 3x+6y=492
Dalton $22 per hour Willard $40 per hour
Dalton $40 per hour Willard $44 per hour
Dalton $62 per hour Willard $62 per hour

1 answer

To solve the problem, we can set up two equations based on the information given:

  1. The relationship between Dalton's hourly pay \( x \) and Willard's hourly pay \( y \): \[ y = x + 22 \]

  2. The total labor cost for both of them based on their hours:

    • Willard worked for 6 hours, and Dalton worked for 3 hours: \[ 6y + 3x = 492 \]

Now, we can simplify the second equation. First, we can substitute \( y \) in the second equation:

Substituting the first equation into the second: \[ 6(x + 22) + 3x = 492 \]

Expanding this: \[ 6x + 132 + 3x = 492 \]

Combining like terms: \[ 9x + 132 = 492 \]

Subtracting 132 from both sides: \[ 9x = 360 \]

Dividing by 9: \[ x = 40 \]

Now we can find Willard's pay \( y \): \[ y = x + 22 = 40 + 22 = 62 \]

Now we have computed both hourly wages:

  • Dalton's hourly pay = $40
  • Willard's hourly pay = $62

Finally, let's match our findings with the chosen equations and potential answers. The viable equations from the options include:

  1. \( y = x + 22 \)
  2. \( 6y + 3x = 492 \)

And the viable pair of answers is:

  • Dalton $40 per hour
  • Willard $62 per hour

So, the correct selections are:

  1. \( y = x + 22 \) and \( 6y + 3x = 492 \)
  2. Dalton $40 per hour and Willard $62 per hour