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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. Kingsbury'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 a job for a customer

Select the two equations that can used be together to answer this question and select the two viable answers based on the given constraints.

1 answer

To solve the problem, we start by formulating the two equations based on the details provided.

  1. Relationship between Willard's and Dalton's hourly pay: Since Willard earns $22 more than Dalton, we can express this relationship as: \[ y = x + 22 \]

  2. Total labor cost equation: Willard worked for 6 hours, and Dalton worked for 3 of those hours. The total labor cost was $492. Therefore, the equation representing the total labor cost can be formulated as: \[ 6y + 3x = 492 \]

Now we have the two equations:

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

Substituting the first equation into the second will help us find the values of \( x \) and \( y \).

Step 1: Substitute \( y \) in the second equation:

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

Step 2: Simplify the equation:

This expands to: \[ 6x + 132 + 3x = 492 \] Combining like terms gives: \[ 9x + 132 = 492 \]

Step 3: Solve for \( x \):

Subtract 132 from both sides: \[ 9x = 492 - 132 \] \[ 9x = 360 \] Dividing both sides by 9 gives: \[ x = 40 \]

Step 4: Find \( y \):

Now we substitute back to find \( y \): \[ y = x + 22 = 40 + 22 = 62 \]

Conclusion:

  • Dalton's hourly pay \( x \) is $40.
  • Willard's hourly pay \( y \) is $62.

Thus, the equations to use are:

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

And the corresponding viable answers are:

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