Mark M. answered • 10/11/16
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Mathematics Teacher - NCLB Highly Qualified
Since water is added the solutions must be in terms of water.
48% solids is 52% water
40% solids is 60% water
0.52(1) + 1.00x = 0.60(1 + x)
Can you solve for x?
Mark M.
Check your division/decimal points.
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10/11/16
Mark M.
If you present work, I can locate any errors.
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10/11/16
Tom M.
0.52 + x = 0.60 + 0.60x
-0.4x = .08 => 0.4x = -.08 => -.02
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10/11/16
Mark M.
0.52 - 0.60 = ?
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10/11/16
Tom M.
I was taught to keep the variables on the left if possible.
0.52 + x = 0.60 + 0.60x
-0.4x = .08
0.4x = -.08
x = -.02
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10/11/16
Mark M.
That's OK, 0.52 - 0.60 = -0.08!
Correct that subtraction.
Be careful with decimals when dividing!
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10/11/16
Tom M.
I wasn't doing 0.52 - 0.60 = -0.08 I was doing 0.60 - 0.52 = .08
0.52 + x = 0.60 + 0.60x (first move 0.60x to the left side)
0.52 - 0.4x = 0.60 (then move 0.52 over to the right side)
-0.4x = .08 (multiple both sides by negative one)
0.4x = -0.08 (then divide -0.08 by 0.4)
x = -0.02
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10/12/16
Mark M.
If you are subtracting (don't use the word "move") 0.60x from the right side, you must subtract 0.60x from the left side.
0.52 + x = 0.60 + 0.60x
0.52 + x - 0.6x = 0.60 + 0.60x - 0.60x
0.52 + 0.4x = 0.60
0.52 - 0.52 + 0.4x = 0.60 - 0.52
0.4x = 0.08
x = 0.2
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10/12/16
Tom M.
Ok thank you. I see where my mistake was.
The answer is 0.2. So I'm suppose to add 0.2 of water to reduce the solids down to 40%.
But what is 0.2? Do we need to convert the gallon into ounces?
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10/13/16
Mark M.
Gallon was the unit of measure in the beginning.
0.2 gallons must be added.
Whether you convert to ounces (or any other measure) depends on the requirement of you teacher.
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10/13/16
Tom M.
10/11/16