Question

Peggy had four times as many quarters as nickels. She had $2.10 in all. How many nickels and how many quarters did she have?

If the variable n represents the number of nickels, then which of the following expressions represents the number of quarters?

The possible answers are:
n/4
n
4n
n + 4

Answer 1

let Q be the number of quarters and N be the number of nickels. Write equations to show the relationships:

"four times as many quarters as nickels"
\[Q = 4*N \]
"$2.10 in all"
Value of quarters = 25Q
Value of nickels = 5N
(I prefer to work in cents rather than dollars, so there are no decimals to bedevil us)
\[25Q + 5N = 210\]

Now solve the system of equations:

\[Q = 4N\]\[25Q+5N =210\]

Do you know how to do that?

Answer 2

I think I do...... Let me try

Answer 3

That's what we like to hear! :-)

Answer 4

Lol

Answer 5

Instead of the all-too-common, whiny "can't you just give me the answer, I don't have much time" :-(

Answer 6

The answer is 4n. Correct?

Answer 7

Why, yes!

Answer 8

Ya... I know what ya mean

Answer 9

Thanks!

Answer 10

How about we solve the whole problem? Just for giggles?

Answer 11

Just wondering..... Are you a man or woman? lol just wondering not like it matters

Answer 12

My friends call me "hey, you", does that help? :-)

Answer 13

Man?

Answer 14

(also, I have a beard)

Answer 15

Oh! Then man

Answer 16

and I'm starring in the circus freak show :-)

Answer 17

lol

Answer 18

math problems done while you watch :-)

Answer 19

:)

Answer 20

so, we have our two equations. have you learned about solving systems of equations yet?

Answer 21

I'm posting another question.

Answer 22

let's finish this one first, then I'll help you with the other one.

Answer 23

Ralph is 3 times as old as Sara. In 4 years, Ralph will be only twice as old as Sara will be then. Find Ralph's age now.

If x represents Sarah's age now, which of the following expressions represents Ralph's age in four years ?

3 x
6 x
2 x + 4
3 x + 4

Answer 24

I'm bad at this stuff...

Answer 25

Ah, but I'm a great teacher, so we'll fix that :-)

Answer 26

So here are our two equations:
\[Q = 4N\]\[25Q + 5N = 210\]

Do you see how I came up with both of those equations?

Answer 27

The problem said we had 4 times as many quarters as nickels, so Q = 4N should be obvious.

Also, the value of our quarters plus the value of our nickels adds up to $2.10, or 210 cents.

If we have 1 quarter, that is worth 25 cents. If we have 2 quarters, 50 cents. In general, if we have Q quarters, the value of the quarters is 25 cents per quarter * the number of quarters, or 25Q. Same for nickels, except there it is 5N.

So our value of coins is 25Q + 5N = 210.

Answer 28

Now, to solve this, we look at our first equation and we see that it gives Q in terms of N, specifically Q = 4N. We rewrite our second equation, replacing "Q" wherever we see it with "4N". This is the substitution step, and why this method is called (wait for it, wait for it..) substitution.

\[25Q + 5N = 210\]\[25(4N) + 5N = 210\]Simplify that a bit\[100N + 5N = 210\]Simplify some more by collecting like terms\[105N = 210\]To solve that for \(N\), we just divide both sides by the number in front of \(N\):
\[\frac{105N}{105} = \frac{210}{105} \]\[N = \frac{210}{105} = \]

Answer 29

Hopefully you agree that is N = 2.

Now we plug N = 2 into our formula Q = 4N
Q = 4(2) = 8

So there are 8 quarters, and 2 nickels. Let's check our answer:

8*25 = 200 cents
2*5 = 10 cents
-----
210 cents (or $2.10)

Our answer is correct!

Answer 30

sorry i didnt reply