Question 150329: Mr. Phillips bought 7 drums of two different cleaning fluids for his dry cleaning business. One of the fluids cost $30 a drum and the other was $20 a drum. The total price of the supplies was $160. How much of each fluid did Mr. Phillips buy? Write a system of equations and solve by graphing.
Answer by mangopeeler07(462)   (Show Source):
You can put this solution on YOUR website! x=$30 drum
y=$20 drum
30x+20y=160
x+y=7
Solve for x
x=7-y
Plug that in
30(7-y)+20y=160
Distribute
210-30y+20y=160
Combine like terms
210-10y=160
Subtract 210
-10y=-50
Divide by -10
y=5
x+y=7
x+5=7
x=2
2 $30 drums
5 $20 drums
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30x+20y=160
x+y=7
These are two lines that you must graph. First, get them into y=mx+b form by isolating y in each.
20y=160-30x
y=8-30/20x
y=-3/2x+8
y=7-x
y=-x+7
Now graph them:
y=-3/2x+8
| Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc |
Equation  describes a sloping line. For any
equation ax+by+c = 0, slope is  .- X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 160/30 = 5.33333333333333.
- Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 160/20 = 8.
- Slope is -30/20 = -1.5.
- Equation in slope-intercept form: y=-1.5*x+8.
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y=-x+7
| Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc |
Equation  describes a sloping line. For any
equation ax+by+c = 0, slope is  .- X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 7/1 = 7.
- Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 7/1 = 7.
- Slope is -1/1 = -1.
- Equation in slope-intercept form: y=-1*x+7.
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Notice that the one point that both lines contain is at (2,5)...(which may be difficult to see on these graphs). Once you graph them on your own, you will see this better. That is how you verify your solution by graphing.
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