Question

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

Answer 1

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

Answer 2

word problems I don't understand much

Answer 3

Okay, let's see if we can change that :-)

Can you tell me how many different kinds of items there are to purchase here?

Answer 4

cds

Answer 5

okay, are they all the same price?

Answer 6

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

Answer 7

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?

Answer 8

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

Answer 9

she spend 114.00

Answer 10

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.

Answer 11

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?

Answer 12

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

Answer 13

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?

Answer 14

114 right

Answer 15

144 I meant do u times it ?

Answer 16

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?

Answer 17

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 \(14y\).

Answer 18

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.

Answer 19

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?