monica has 17 coins in her change purse worth $3.05 if she only has quarters and nickels, how many each does she have?

Question

show all work and answer with substitution or elimanation

Answer 1

I'm gonna deal with cents to get rid of the pesky decimals!

q + n = 17

25q + 5n = 305

First, since we have both q and n with no coefficient, it's easy to solve for either. I'll do n.

n = 17 - q

Now, equal means just that. We can substitute one side for the other.

25q + 5(17 - q) = 305

25q + 85 - 5q = 305

20q = 220

q = 11 quarters

n = 17 - q

n = 17 - 11

n = 6 nickles

Answer 2

Hello Ashley, my name is Katie and I would be happy to help you with your question!

The first step is to define the information in equation form. Since there are only quarters and nickels and we don't know how many of each, let's use q for the number of quarters and n for the number of nickels.

Monica has 17 coins in total, so:

q + n = 17

The total value of the coins is $3.05. Because a quarter equals $0.25 and a nickel equals $0.05. So multiply the value of the coins by the unknown number in variable form and add them together.

($0.25)q + ($0.05)n = $3.05

The next step is to solve for one of the variables for one equation, then use substitution to place that value in the other equation.

q + n = 17

-q -q

n = 17 - q

Substitute 17 - q for n into the second equation, and solve for q.

($0.25)q + ($0.05)(17 - q) = $3.05

Distribute and simplify.

($0.25)q + ($0.05)(17 - q) = $3.05

$0.25q + $0.85 - $0.05q = $3.05

$0.20q + $0.85 = $3.05

-$0.85 -0.85

$0.20q = $2.20

$0.20 $0.20

q = 11

To find the value of n, substitute 11 in the first equation for q

q + n = 17

11 + n = 17

-11 -11

n = 6

To check your answer, put both values into the second equation and check your answer.

($0.25)q + ($0.05)n = $3.05

($0.25)(11) + ($0.05)(6) = $3.05

$2.75 + $0.30 = $3.05

$3.05 = $3.05

That is correct so you know q = 11 and n = 6 is the correct answer.

Please send me a message or comment if you have any further questions or would like a tutoring session!

Answer 3

Hello, Ashley,

Let's assign the number of quarters and nickels to the letters Q and N.

We are told that Q + N = 17.

The total amount is $3.05. Let's use pennies, since I get tired of decimal points everywhere. So we can make an equation that adds the quarters (at 25 each) and nickels (at 5 each) and set that equal to 305 (pennies).

25Q + 5N = 305

Now rearrange the first equation by isolating N: N = 17-Q

Now use this in the second equation, substituting 17-Q for N

25Q +5(17-Q) = 305

25Q + 85 - 5Q = 305

20Q = 220

Q = 11

That means N = 6

See if 11 quarters and 6 nickels add up to 305 pennies.

11*25 = 275

6*5 = 30

305

That works,

Bob