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Tony worked 6 hours more than Carl last week. Together, the two boys worked a total of 58 hours.

Using elimination, how many hours did each of them work?

Answer :

Final answer:

Therefore, Tony worked 32 hours, and Carl worked 26 hours.

Explanation:

Let's solve the problem where Tony worked 6 hours more than Carl last week, and together they worked a total of 58 hours using the elimination method in algebra.

Firstly, we'll define two variables for the hours worked by Tony and Carl:

  • Let T be the number of hours Tony worked.
  • Let C be the number of hours Carl worked.

According to the problem, we have two equations:

  1. Tony worked 6 hours more than Carl: T = C + 6
  2. Together, they worked 58 hours: T + C = 58

Now, let's use the elimination method:

  1. Subtract the second equation from the first:
    (C + 6) + C = 58
  2. 2C + 6 = 58
  3. Subtract 6 from both sides: 2C = 52
  4. Divide both sides by 2: C = 26
  5. Now, substitute C back into the first equation: T = 26 + 6
  6. T = 32

Therefore, Tony worked 32 hours, and Carl worked 26 hours.

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