At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
Can you write the two equations that express the information we know?
word problems I don't understand much
Okay, let's see if we can change that :-) Can you tell me how many different kinds of items there are to purchase here?
okay, are they all the same price?
Sabrina bought 9 CDs and some was 14 and some was 12
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?
how about \[x+y=9\]?
she spend 114.00
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.
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?
I have covered all that but I have forgot how to use them.
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?
144 I meant do u times it ?
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?
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 \(14y\).
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.
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?