Solve each problem using a system of equations. A company sell...

Question

Solve each problem using a system of equations. A company sells recordable CDs for $0.80 each and play-only CDs for $0.60 each. The company receives $76.00 for an order of 100 CDs. However, the customer neglected to specify how many of each type to send. Determine the number of each type of CD that should be sent.

Accepted Answer

Hello everybody. I have everything right today. Today, we're going to look at this question that states a pharmacy sells a ayin for $$10 per tablet and amoxicillin for 15 $$per tablet. The pharmacy receives an order for 50 tablets but the customer forgot to specify how many of each item to send. Now, if the pharmacy receives $$650 for the order, how many tablets of Ayin and amoxicillin should they send the ATO is provide us with a choice. A being Azithromycin 20 and Amox Aid in 30 B is Azithromycin 30 and amoxicillin 20 C is Azithromycin 10 and Amoxin in 40 N D is Azithromycin 40 and amoxicillin 10. Now, the first thing I'll do here is assign a variable to each one of my tablets. So I'm going to say that X is equal to the tablets of A and instead of saying every time I'm going to abbreviate as A Z and Y will be equal to the tablets of amoxicillin. And I'll call this am. Now, they told us that A Zithromycin is 10 $$per tablet. So we'll have that the cost of X tablets is equal to 10 X because $$10 per tablet. And we have the tablet as X. So we have 10 X and then the cost of Y tablets, they told us that amoxicillin is 15 $$per tablet. So we have 15 win. So now we can create two different formulas. I'm gonna call formula number one will be the total order or the total number of tablets. So we have that X plus Y is equal to 50. And equation number two will be dealing with the total cost of the tablets. So we have that 10 X plus 15 Y is equal to 650. So now I write both. What I, what I've done is I've written both equations one on top of the other because I'm going to use a technique called elimination. So I'm going to multiply equation number one by negative 10. And that will give me equation number one will not be negative 10 X or minus negative 10 X. So we have negative 10, X minus 10 Y is equal to negative 500. And equation number two will remain the same and I'll put it right under equation number one to have 10, X plus 15 Y it's equal to 650. So why do I write them one on top of the other? Well, for elimination, what we're going to try to do is basically eliminate one of the variables. And that's why I multiplied equation number one by negative 10 because now I put both equation on top of the other and imagine we're adding them up. So I put them on top of the other. Because when we're doing addition, that's usually what we're taught, we put one number on top of the other and we add them up with the line. So we do the same thing with our equations. And if we multiply the equation number one by negative 10, we have negative 10 X on top and we're adding a 10 X on the bottom. So the X variable cancels out and then we'll have negative 10, Y plus 15, Y will be five, Y is equal to negative 500 plus which is 150. And then to get the Y, all we have to do is divide both sides by five. And when we left with Y is equal to tablets of AM and that'll be our answer. Our first answer or why or the metabolism of amoxin. So now we can plug this into our X plus Y equation. So we have that X plus Y is equal to 50 and we have Y so we have that X plus 30 is equal to and we can isolate the X by subtracting 30 from both sides. So we have that X is equal to 50 minus 30 which is tablets of A Z. And that'll be our answer for X and for the number of tablets of azithromycin. So this matches up with answer choice, a 20 tablets of Azithromycin and 30 tablets of amoxicillin. So I hope that was helpful. And until next time.

Key Concepts

Systems of Linear Equations

Setting Up Equations from Word Problems

Solving Systems by Substitution or Elimination

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