Polynomial word problem: total value of bills
About this video
Sal writes a polynomial for the total value of p $20 bills, q $10 bills and r $5 bills. Each kind of bill is worth its value times how many there are, giving 20p + 10q + 5r, a polynomial with three terms (a trinomial).
You'll be able to
- write an expression for the value of a number of bills of the same kind.
- add terms to write a polynomial for a total value.
- explain what polynomial and trinomial mean.
Key words
- polynomial
- An expression made of terms added or subtracted together, such as 20p + 10q + 5r.
- trinomial
- A polynomial with exactly three terms.
- term
- One part of an expression separated by + or -, such as 20p.
Transcript
Write a polynomial to express the total value of p $20 bills, q $10 bills, and r $5 bills. So what's the value of p $20 bills? Well if I have p $20 bills, the value of each of those dollar bills is going to be $20. So the value all p of them is going to be 20p.
If I have one $20 bill, it's $20. If I have three $20 bills, if p is 3, it's going to be $60. Actually, let me do that in the same color as I underlined it. I underlined it in yellow. So let me do the p $20 bills. So 20p is the p $20 bills. Then you have your q $10 bills.
So what's the value of those? Well it's going to be 10q. If I have one $10 bill, it's worth $10. If I have ten $10 bills, if q is 10, this is going to be worth 10 times 10. $100. And then finally you have your r $5 bills, which are going to be worth 5r dollars.
One $5 bill, worth $5. Two $5 bills, worth $10. And we're done. We've expressed it as a polynomial. Polynomial just means that we have multiple terms here and this is three terms. We could even call it a trinomial. Polynomial is a more general term for more than one term.
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