At a local electronics store, CDs were on sale. Some were priced at $14.00 and some at $12.00. Sabrina bought 9 CDs and spent a total of $114.00. How many $12.00 CDs did she purchase?
Select one:
a. 5
b. 3
c. 6
d. 9

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- schrodinger

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- whpalmer4

Can you write the two equations that express the information we know?

- anonymous

word problems I don't understand much

- whpalmer4

Okay, let's see if we can change that :-)
Can you tell me how many different kinds of items there are to purchase here?

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## More answers

- anonymous

cds

- whpalmer4

okay, are they all the same price?

- anonymous

Sabrina bought 9 CDs and some was 14 and some was 12

- whpalmer4

Okay, so there are two different choices, $12 CDs and $14 CDs. Let's call the $12 CDs \(x\), and the $14 CDs \(y\) — those variables represent how many of each she bought.
We know that she bought 9 CDs in all. Can you write an equation using \(x\) and \(y\) and \(9\) that says that?

- whpalmer4

how about \[x+y=9\]?

- anonymous

she spend 114.00

- whpalmer4

Before we go on, have you learned how to solve systems of equations with more than one variable? Or do you always have just one variable? There are a couple of ways to do this, and I don't want to use material that you haven't covered yet.

- whpalmer4

right now, we just want an equation that tells us how many CDs were purchased, we don't know yet the breakdown.
\[x+y= 9\]tells us that some number of $12 CDs (represented by \(x\)) and some number of $14 CDs (represented by \(y\)) were purchased, and together there were 9 CDs. That's the situation we have here, right?

- anonymous

I have covered all that but I have forgot how to use them.

- whpalmer4

No problem. I still remember :-)
Now, if we say that \(x\) is the number of $12 CDs we buy, how much money do we spend on $12 CDs, as an expression?

- anonymous

114 right

- anonymous

144 I meant do u times it ?

- whpalmer4

No, you're getting ahead of yourself — we don't know how many $12 CDs we bought, just that we have a variable named \(x\) which represents that number, whatever it turns out to be.
If you buy 1 $12 CD, how much do you spend on $12 CDs?

- whpalmer4

You spend 1*$12 = $12. If you buy 2, you spend 2*$12 = $24. Etc. In general, to buy \(x\) $12 CDs, you spend $\(12x\), right? We'll just call that \(12x\) and remember that we are talking about prices in dollars.
Similarly, the $14 CDs we called \(y\), so we spend $\(14y\) on $14 CDs, and again we will simplify that to \(14y\).

- whpalmer4

We know that we spent $114 on 9 CDs which cost either $12 or $14. We can write two equations to express that information.
\[x+y = 9\]This shows that we purchased 9 CDs of one type or the other\[12x+14y=114\]This shows that the amount spent of those CDs ($12 and $14 per CD, respectively) totals $114.

- whpalmer4

Our system of equations is
\[x+y=9\]\[12x+14y=114\]
Do you know how to solve that now that we have figured out what the word problem is asking?

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