Question 77642: In my algrebra class, we are currently solving word problems using graphing, substitution, or elimination. I have one question that I am absolutely stumped on. I cant figure out how to even begin to set the problem up. Here is the problem: A pastry chef created a 50ounce sugar solution that was 34% sugar from a 20% sugar solution and a 40% sugar solution. How much of the 20% sugar solution and how much of the 40% sugar solution were used? Can you please help me? ~Brandi~
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! These "mixture" problems can sometimes be a little perplexing!
It is helpful to think about how much sugar there is in each of the mixtures
In the 50 ounces of 34% sugar solution you have 34% of 50 ounces of sugar. That's 0.34(50) = 17 ounces of sugar.
This is made up of x ounces of 20% sugar solution or 0.2x ounces of sugar, plus (50-x) ounces of 40% sugar solution or 0.4(50-x) ounces of sugar.
Now you can make an equation to solve for x, the amount of 20% sugar solution.
0.34(50) = 0.2x + 0.4(50-x) Simplify and solve for x.
17 = 0.2x + 20 - 0.4x Combine like-terms.
17 = 20-0.2x Subtract 20 from both sides.
-3 = -0.2x Divide both sides by -0.2
15 = x
So, you would need 15 ounces of 20% sugar solution plus (50-15) = 35 ounces of 40% sugar solution to obtain 50 ounces of 34% sugar solution.
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