anonymous
  • anonymous
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
Algebra
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anonymous
  • anonymous
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
Algebra
schrodinger
  • schrodinger
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whpalmer4
  • whpalmer4
Can you write the two equations that express the information we know?
anonymous
  • anonymous
word problems I don't understand much
whpalmer4
  • 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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anonymous
  • anonymous
cds
whpalmer4
  • whpalmer4
okay, are they all the same price?
anonymous
  • anonymous
Sabrina bought 9 CDs and some was 14 and some was 12
whpalmer4
  • 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
  • whpalmer4
how about \[x+y=9\]?
anonymous
  • anonymous
she spend 114.00
whpalmer4
  • 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
  • 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
  • anonymous
I have covered all that but I have forgot how to use them.
whpalmer4
  • 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
  • anonymous
114 right
anonymous
  • anonymous
144 I meant do u times it ?
whpalmer4
  • 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
  • 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
  • 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
  • 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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