Reminder: Word Problem Stratigies (mixtures/investments)

Ok, I can see loads of people are having trouble with some of the word problems. I was having problems with the fertilizer questions until I went back in my notes and realized the antifreeze example/question we went through in class is exactly the same. Then I experimented with the other questions in the same fashion and It wasn't too hard. I'll go through the antifreeze question (that we all should have in your notes).

Ex) Antifreeze A is 18% alcohol. Antifreeze B is 10% alcohol. How many liters of each should be mixed to get 20L of a mixture of 15% alcohol?

Step 1: Create Let Statements (be specific!)
Let a = the number of liters required of the 18% solution
Let b = the number of liters required of the 10% solution

Ask yourself... "what am I solving for?"

Step 2: Create two equations with two variables in each
L1: a + b = 20
L2: 0.18a + 0.10b = 0.15(20)

The second statement is basically (based on the let statements):
type of the first solution times liters of that solution + type of the second solution times liters of that solution = type of mixture you want times liters of the solution you want.

Maybe thinking of it like that will help y'all (I'm sure that's how Mr. Max has been saying it), instead of... point eighteen times 'a' plus point ten times 'b' equals point fifteen times twenty.

Step 3: Solve
The easiest way would be to throw it in graphmatica, but I didn't have graphmatica handy so the next easiest way was within my calculator (let's just go down the line from easiest to hardest).

I'm going to isolate b (the number of liters required of the 10% solution).
L1: b = 20 - a
L2: b = (3 - 0.18a)/0.10

I got L2 this way:
0.18a + 0.10b = 0.15(20)
0.18a + 0.10b = 3
0.18a + 0.10b - 0.18a = 3 - 0.18a
0.10b/0.10 = (3 - 0.18a)/0.10
b = (3 - 0.18a)/0.10

Remember ;)
2nd, CALC, 5: (intercept), ENTER * 3

Step 4: Create a statment to summarize your answer.
In order to create 20L of 15% alcohol antifreeze, mix 12.5L of 18% with 7.5L of 10% antifreeze.

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All raw information came from our lesson in class and out of my keyboard


:)