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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:
- Tony worked 6 hours more than Carl: T = C + 6
- Together, they worked 58 hours: T + C = 58
Now, let's use the elimination method:
- Subtract the second equation from the first:
(C + 6) + C = 58 - 2C + 6 = 58
- Subtract 6 from both sides: 2C = 52
- Divide both sides by 2: C = 26
- Now, substitute C back into the first equation: T = 26 + 6
- T = 32
Therefore, Tony worked 32 hours, and Carl worked 26 hours.
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