brody is working two summer jobs, making $10 per hour babysitting and making $15 per hour cleaning tables. In a given week, he can work a maximum of 13 total hours and must earn at least $150. If x represents the number of hours babysitting and y represents the number of hours cleaning tables, write and solve a system of inequalities graphically and determine on possible solution.
Answers
The solution is x = 9 and y = 4, meaning Brody would work 9 hours babysitting and 4 hours cleaning tables to satisfy both conditions (total hours ≤ 13 and total earnings ≥ $150).
Given:
Brody can work a maximum of 13 hours: x + y ≤ 13
Brody must earn at least $150: 10x + 15y ≥ 150
These are the two inequalities we need to solve graphically.
Graph the first inequality: x + y ≤ 13
This inequality represents the total number of hours Brody can work, which cannot exceed 13 hours. We'll plot the line x + y = 13 and shade the region below it.
Graph the second inequality: 10x + 15y ≥ 150
This inequality represents the total earnings Brody needs to make, which should be at least $150. Let's simplify it to 2x + 3y ≥ 30. We'll plot the line 2x + 3y = 30 and shade the region above it.
Now, let's find the point where the shaded regions of both inequalities overlap. This point will represent the feasible solution where Brody's working hours and earnings satisfy both conditions.
Solving the system of inequalities graphically, you will find the point of intersection. However, since I can't create a graphical representation here, I'll explain how to calculate the solution point algebraically:
First, solve the equation x + y = 13 for y:
y = 13 - x
Now substitute this value of y into the equation 2x + 3y = 30:
2x + 3(13 - x) = 30
2x + 39 - 3x = 30
-x = -9
x = 9
Now substitute the value of x back into the equation y = 13 - x:
y = 13 - 9
y = 4
So, the solution is x = 9 and y = 4, meaning Brody would work 9 hours babysitting and 4 hours cleaning tables to satisfy both conditions (total hours ≤ 13 and total earnings ≥ $150).
To know more about inequalities:
#SPJ3
Graph y≤13−x (shading down)
graph y≥10− 3/2x (shading up)
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Answers
Answer: L=45, W=9
Step-by-step explanation:
Perimeter P=108 so if L=5W,
P=2(L+W)=2(5W+W)=2(6W)=12W
108=12W
W=108/12=9
L=5*9=45
Answers
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closed questions are questions with fixed answer options
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Answers
.. n + 7
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The temperature at 10 am was 72° +13° = 85°.
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The difference is,
EXPLANATION
To find the difference, we just have to simplify the expression.
The given expression is
We factor the denominator of the second fraction to get,
We can now see clearly that the LCM is
We collect LCM to get,
We now expand the bracket to obtain,
This gives us,
(x +5)/ (x +2) - (x + 1)/(x ^2 + 2x)
=(x +5)/ (x +2) - (x + 1)/[x (x + 2)]
the LCM is x(x+2)
thus the difference will be:
[x(x+5)-(x+1)]/(x (x + 2))
=[x^2+5x-x-1]/[x(x+2)]
=(x^2-4x-1)/[x(x+2)]
Answer:(x^2-4x-1)/[x(x+2)]