SOLUTION: I am stuck on trying to figure out trying to write out the equation to solve it. It says Charlene is earning money to buy a new I-phone. She makes $10 per hour babysitting and $5 p

Question 1024760: I am stuck on trying to figure out trying to write out the equation to solve it. It says Charlene is earning money to buy a new I-phone. She makes $10 per hour babysitting and $5 per hour gardening. She wants to make at least $80 each week. She can work no more than a total of 12 hours in a week. How many hours doing each jib will earn the most money each week?
Found 2 solutions by stanbon, rothauserc:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Charlene is earning money to buy a new I-phone. She makes $10 per hour babysitting and $5 per hour gardening. She wants to make at least $80 each week. She can work no more than a total of 12 hours in a week. How many hours doing each jib will earn the most money each week?
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Equations:
Hours Eq::: b + g = 12
Value Eq:::10b + 5g = 80
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Modify for elimination::
b + g = 12
2b + g = 16
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Subtract and solve for "b"::
b = 4 (# of hours babysitting)
g = 12-g = 8 hrs (# of hours gardining)
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Cheers,
Stan H.
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Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
10x + 5y > or = 80
x + y < or = 12
:
solve each inequality for y
:
y > or = 16 -2x (red line)
y < or = 12 -x (green line)
:
consider the graph
:

:
we consider the area of the graph where the two inequalities overlap
:
this is the area bounded by the three points (4,8), (8,0), (12,0) which represents money earned by Charlene
:
******************************************************************************
check each endpoint of the area
10(4) + 5(8) = 80
10(8) + 5(0) = 80
10(12) + 5(0) = 120
:
Charlene maximizes the money she earns in a week by working 12 hours babysitting and 0 hours gardening
******************************************************************************
:

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