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Question 174662This question is from textbook Glencoe Algebra 1 Volume Two
: It's kind of like a question. They solve it and such, but the steps in which they solved it is unclear. I am hoping that you'll make it clearer to me. it would be greatly appreciated. I'll type the whole question to you.
...this is the question...
-Unita likes her job as a baby-sitter, but it pays only $3 per hour. She has been offered a job as a tutor that pays $6 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week. How many hours can Unita tutor and baby-sit and still make at least $65 per week?
...then it goes on to explain...
Let x represent the number of hours Unita can baby-sit each week. Let y represent the number of hours she can tutor each week. Since both x and y represent a number of hours, neither can be a negative number. Thus, x -greater or equal to 0 and y is greater or equal to 0. Then the following systems of inequalities can be used to represent the conditions of this problem.
...then it goes on further...
x is greater or equal to 0
y is greater or equal to 0
3x + 6y is greater or equal to 65
x + y is less than or equal to 15
-i regret to tell you i can't send you the picture of the graph. Now my question is, how did they take that information and place it into the graph? I await your answer with great anticipation. Also i ask that you to explain it to me as if i was a five year old -no offense to you it's just my mind is slow to accumulating information quickly- Thank you again!
This question is from textbook Glencoe Algebra 1 Volume Two
Found 2 solutions by nerdybill, stanbon:
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! x is greater or equal to 0
Because, 'x' represents the number of hours Unita baby-sat, it has to "equal to or greater" than zero because you can't work for "negative hours".
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y is greater or equal to 0
Similarly, because 'y' represents the number hour Unita tutored -- it has to "equal to or greater" than zero because you can't work for "negative hours".
.
Since there are two variables -- x and y -- we'll need to find two expressions or formulas.
.
The first formula deals with the amount of money she makes:
That is, "total earned by baby-sitting" plus "total earned tutoring" has to be "greater or equal" to $65.
3x + 6y >= 65
The expression on the left side is the "total amount" Unita earned by baby-sitting and tutoring. For example, since she gets $3 per hour for baby-sitting, the amount earned is 3 times the number of hours she baby-sat (which is 'x'). The same for 6y.
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The second formula deals with the total number of hours Unita worked:
That is, "total hours baby-sitting" plus "total hours tutoring" has to be "less than or equal" to 15 hours.
x + y <= 15
This expression represents hours
Since her parents is allowing her to work a MAXIMUM of 15 hours, the hours worked baby-sitting plus the hours worked tutoring has be "less than or equal" to 15.
.
The graph represents these two formulas. The first:
3x + 6y >= 65
Manipulate to "slope-intercept" form:
6y >= -3x + 65
y >= (-3/6)x + 65/6
y >= (-1/2)x + 65/6
graping this line: slope=(-1/2) and y-intercept at (0, 65/6)
Since it is >= the line is SOLID and you SHADE the area ABOVE this line.
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The second:
x + y <= 15
Manipulate to "slope-intercept" form:
y <= -x + 15
graping this line: slope=(-1) and y-intercept at (0, 15)
Since it is <= the line is SOLID and you SHADE the area BELOW this line.
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Where the two shaded regions OVERLAP are the possible values for x and y.
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Write back if you still have questions.
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! -Unita likes her job as a baby-sitter, but it pays only $3 per hour. She has been offered a job as a tutor that pays $6 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week. How many hours can Unita tutor and baby-sit and still make at least $65 per week?
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Let x represent the number of hours Unita can baby-sit each week. Let y represent the number of hours she can tutor each week. Since both x and y represent a number of hours, neither can be a negative number. Thus, x -greater or equal to 0 and y is greater or equal to 0. Then the following systems of inequalities can be used to represent the conditions of this problem.
Earnings Inequality: 3x + 6y >= 65
Rearranging that you get : y >= (-1/2)x + (65/6)
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x >= 0
y >= 0
The above two inequalities restrict the graph to the 1st quadrant.
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Quantity Inequality: x + y <= 15
Rearranging that you get: y <= -x + 15
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-i regret to tell you i can't send you the picture of the graph. Now my question is, how did they take that information and place it into the graph?
They graphed
y >= (-1/2)x - (65/6) and
y <= -x+15
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Cheers,
Stan H.
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