Question

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Penelope and Artemis worked a total of 70 hours this week. Penelope worked 2 hours less than twice what Artemis worked.

1) Let P= hours Penelope worked and A= hours Artemis worked. Write a system of equations for this scenario.

2) Determine how many hours Penelope and Artemis worked.

Answer 1

P + A = 70

2P = A + 2

1) P + A = 70

2P = A + 2

2) Solve the system of equations:

Subtract P from both sides of the first equation:

A = 70 - P

Substitute A for 70 - P in the second equation:

2P = (70 - P) + 2

Simplify:

2P = 72 - P

Add P to both sides of the equation:

3P = 72

Divide both sides of the equation by 3:

P = 24

Substitute P for 24 in the first equation:

A = 70 - 24

A = 46

Penelope worked 24 hours and Artemis worked 46 hours.