SOLUTION: Please help me. I'm not sure I know what I'm doing. You bought 12 one-gallon bottles of apple and orange juice for a school dance. The apple juice was on sale for $1 per bottl

Question 189411: Please help me. I'm not sure I know what I'm doing.
You bought 12 one-gallon bottles of apple and orange juice for a school dance. The apple juice was on sale for $1 per bottle and the orange juice was on sale for $1.50 per bottle. All together you only spent $15. How many bottles of each type did you buy?
My answer:
Variables: C # of bottle of Apple Juice Equation 1: C + D = 12
D # of bottles of Orange Juice Equation 2: 1c+$1.50D=15
C+D=12 C+15 0D=15
-D=0 (-D+12)+$1/5-D=15
a-D+17 $.50D+12=15
-12 -12
506/50=3/50
b=6
Thank you so much.

Found 2 solutions by solver91311, greta_elisif:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

I had a great deal of trouble following how you worked this, but I can say this: Your equations are set up correctly, and to the extent that your "b=6" at the very end really means "D = 6" then you also got the right answer for half of the question. Quite obviously C would have to equal 6 as well if they are going to sum to be 12. Given that, nothing else really matters. Good job.

John

Answer by greta_elisif(10) (Show Source): You can put this solution on YOUR website!
First mistake: mixed up notation.
Please keep your equations and the application of them separate. Your understanding will be clearer and your teacher will be happier. Since equations are abstract, the only things that belong in them are abstract symbols. Use lower-case variables in algebra. C does not equal c.
This is the way to set up the problem:
= number of bottles of apple juice
= number of bottles of orange juice

or
Then it is solved like this: ( doesn't equal zero)

Replace in the other equation with your result (zero times anything equals zero). It is solved like this:

Second mistake: you didn't answer the question. This is related to the first mistake. To solve a word problem, translate the information in it to algebraic notation first, so make it abstract. Then you have to make it concrete again. So translate your result to its application or meaning. When you are at this point in the problem, go back to the question and ask, "What do I have to find?" Then you look at your result and see what it says about that and formulate your answer. Sometimes more than one thing is required, like here. We have found there were 6 bottles of orange juice bought. This equation lets you find the number of apple juice bottles bought.

Your answer is, "I bought 6 bottles each of apple and orange juice."
I've seen a lot of these mistakes before, so I think they are common, probably caused by a (very unfortunate) lack of rigor and logic in schools.
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