**Q = 53**[divide both sides by (-20)]

**N = 27**[divide both sides by (-1)]

**Q = 53**

**N = 27**

Using elimination or subsistution

Tutors, sign in to answer this question.

Choose appropriate variables (either x and y, or N and Q, or other). Let:

N = number of nickels

Q = number of quarters

Now, realize that the value of the nickels is 5N and the value of the quarters is 25Q.

Translate:

"containing 80 coins " means N+Q = 80 [eq1]

"total value of the coins is $14.60" means 5N + 25Q = 1460 [eq2]

[note: It is easier to use cents than to keep the decimal point]

The math:

(1) elimination - the coefficient of one of the variables must be the same (or opposite) to subtract (or add) the equations.

5N + 5Q = 400 [5*eq1]

5N + 25Q = 1460 [eq2]

---------------------------------- [elimination; subtract equations]

-20Q = -1060

N + Q = 80 [eq1 again]

------------------------------- [elimination; subtract equations]

-N = -27

Check:

Is 5*27 + 25*53 = 1460 ?

135 + 1325 = 1460 ?

1460 = 1460 ?yes

(2) substitution - isolate (solve) for one variable in terms of the other in one equation, then substitute that into the other equation

N = 80 - Q [from eq1]

5(80-Q) + 25Q = 1460 [substitute for N in eq2]

400 - 5Q + 25Q = 1460

400 + 20Q = 1460

20Q = 1060

Now, substitute for Q in either equation:

N + 53 = 80 [eq1 is pretty easy]

[note: same check applies]

*Let n be the number of nickels. *

*Let q be the number of quarters. *

We are told: q + n = 80 ,call this equation1

Also we know the dollar values: 0.25q + 0.05n = 14.60 ,call this equation2

Let's simplify equation1 and get, n = 80 - q

Let's plug n into equation2 and get, 0.25q + 0.05(80-q) = 14.6

Let's expand and get, 0.25q + 0.05*80 - 0.05*q =14.6

This simplifies to: 0.25q + 4 - 0.05q =14.6

Bring like terms together and get: 0.25q - 0.05q =14.6 - 4

This simplifies to: 0.20q = 10. 6

Solve for q and get, q = 10.6/0.20 = 53

From equation1 we know: q + n =80, Let's plug in q=53 and get, 53 + n = 80

Let's solve for n and get, n = 80 - 53 = 27

**Answer: So we have 27 nickels and 53 quarters. **

Extra step: Let's check our answer by using equation2:

0.25*53 +0.05*27 = 13.25+1.35 = 14.60

Our calculated 14.6 = 14.6 from equation2.

So we are correct!

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Karen M.

Certified ADHD Life Coach specializing in Academics

$11.25 per 15 min

View Profile >

Chris J.

Experienced Math and Chemistry Tutor

$11.25 per 15 min

View Profile >

Keri B.

Experienced and patient teacher: ESL, Algebra, K-6, and GED qualified

$10 per 15 min

View Profile >

## Comments

Detail-orientedTutor for Math, Science, English, Coding and Test Prep"