Test Your Skills at MONEY with LETTERS.

This lesson takes a favorite topic, money, and gives is a decidedly "algebraic" twist.

The trick is to read each problem carefully and decide what coin you know NOTHING about. That is the coin that you call "x",or any variable you like. Once you've defined the "mystery coin" with a variable, you can develop an expression for the other coin or coins, using the information given in the problem.

It actually turns out to be like solving a mystery puzzle by being given only a few clues. After you get the hang of using the variables to help you solve the "mystery", it gets fun.

Sometimes you will read a problem that truly sounds as though it doesn't have enough information to be solved. It never ceases to amaze us how even these seemingly impossible problems can be crushed with the power of a well defined variable.

Examine the two samples we offer below; then try a few on your own. Challenge yourself not to click the answer links until you have an answer on your own. (It will spoil the feeling of triumph if you look first.)

---

EX1: Mindy has 3 times as many nickels as dimes. The coins have a total value of $1.50. How many of each coin does she have?

Well now let's see, what do we know nothing about? (Read the problem over to yourself asking that question.)

We know Mindy has 3 times more nickels than dimes, but we don't know anything at all about the number of dimes. So we will let the number of dimes be our "mystery number" and we will call it "d" for dimes.

Now the number of nickels will be 3 times more than d, or 3d.

No. of nickels = 3d
No. of dimes = d

It says the coins have a total value of $1.50. Each nickel is worth 5 cents and each dime is worth 10 cents, so we can put these clues together to make this equation:

5(3d) + 10(d) = 150
*Be careful here to set the total amount of money to CENTS not dollars. We have to do this because we have used the 5 and the 10 to represent the value of each nickel and dime. If you really need to use $ notation, you would need to use .05 and .10 in the equation. Then the equation would look like this:
.05(3d) + .10(d) = 1.50.

Back to solving the mystery.
5(3d) + 10(d) = 150

15d + 10d = 150
25d = 150
25d/25 = 150/25
1d = 6
So there are 6 dimes worth $.60.

3d = 3(6) = 18
So there are 18 nickels worth $.90.

This is great because $.60 + $.90 = $1.50. So our work checks out!

EX2: Bill Gates took 30 coins to the automatic coin counting machine. He knew he only had dimes and quarters. The machine counted his money and gave him $4.20. How many of each coin did he have?

Once again, let's see what we DON"T know. (READ it over a couple of times.) Okay, we don't know anything about either dimes or quarters, except that they add to 30 total coins.

Well terrific! It turns out that THAT will be sufficient to set up a crusher algebra equation. Watch:

Let either dimes or quarters be represented by a variable. We will arbitrarily choose quarters and let "q" stand for the number of quarters.

Now if "q" is the number of quarters, there has to be "30 - q" dimes. This is because there are only 30 coins total, and if we remove all of the quarters, we will be left only with dimes.

We also know that the value of the coins was $4.20 or 420 cents. So lets make the equation:

No. of quarters = q
No. of dimes = 30 - q

25q + 10(30 - q) = 420

Solving by first multiplying and simplifying the left side of the equation we get.

25q + 300 -10q = 420
15q + 300 = 420

Now subtract 300 from both sides.

15q = 120

Now divide both sides by 15.

q = 8
So there are 8 quarters worth $2.00.

30 - q = 30 - 8 = 22
So there are 22 dimes worth $2.20.

Again this checks because $2.00 + $2.20 = $4.20.

---

Now you guys give these a shot.

1. Carlos Santana has 21 coins in nickels and dimes. Their total value is $1.65. How many of each coin does he have?
2. Kid Rock has $124 dollars in ones and fives in his pocket. While sitting at the Grammy's, he keeps running his fingers over the bills, because he is nervous. He knows he has 8 more $5 bills than $1 bills. How many of each does he have?
3. Salt Lick bought some 20 cent candy and some 25 cent candy. He bought 32 pieces in all, and paid $7.40 for them How many pieces of each kind did he buy?

ANSWERS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANSWERS:

1.) 9 nickels and 12 dimes

2.) 14 ones and 22 fives

3.) 20 (25 cent pieces) and 12 (20 cent pieces)

BACK