#### Question

# How would I solve this math problem?

"George has 35 coins in his pocket, consisting of nickels, dimes and quarters. The monetary sum of the coins is $3.25. There are four times as many nickels as quarters and half as many dimes as nickels. Find the number of each. Define your variables and write a concluding statement. Show your work."

I've been trying to solve it, and every time my work will show that there's twenty quarters, ten dimes and five nickels. Yet, it doesn't correspond with the fact that they have to add up to $3.25.

The equations I made were:

D = number of times, N = number of nickels, Q = number of quarters

Q = 4N, D = 2N

D + N + Q = 35

0.10D + 0.05N + 0.25Q = 3.25

What am I doing wrong? Are my equations correct?

Thanks for any input! :)

#### Answer

A nickels

B dimes

C quarters

A + B + C = 35

A * 0.05 + B * 0.1 + C * 0.25 = 3.25

A = 4C

A = 2B

Therefore, B = A/2 and C = A/4

A + (A/2) + (A/4) = 35

A * (1 + 1/2 + 1/4) = 35

A * (4/4 + 2/4 + 1/4) = 35

A * (7/4) = 35

A = 35 * (4/7)

A = 20

There are 20 nickels, 10 dimes, 5 quarters. It turns out that we only needed the second formula to confirm our result:

20 * 0.05 + 10 * 0.1 + 5 * 0.25 =>

1 + 1 + 1.25 =>

3.25

confirmed.

i suck at math

nickels = x

quarters = x/4

dimes = x/2

No. of nickels—x:

5x + 25(x/4) + 10(x/2) = 325 multiply each side by 0.8 to eliminate fractions

4x + 20(x/4) + 8(x/2) = 260

4x + 5x + 4x = 260

13x = 260

x = 260/13 or 20

No. of quarters:

= 20/4 or 5

No. of dimes:

= 20/2 or 10

Answer: nickels, 20; dimes, 10; quarters, 5

Check:

= $0.05(20) + $0.10(10) + $0.25(5)

= $1.00 + $1.00 + $1.25

= 3.25

The question is probably wrong. The correct monetary sum of the coins may be $3.75.

No. of nickels = x and the value of each nickel = 5 cents ; value of nikels = 5x cents.

No. of quarters = 4x and the value of each quarter = 25 cents ; value of quarters = 100x cents.

No. of dimes = 2x and the value of each dime = 10 cents ; value of dimes = 20x cents

Total monetary value = (5x + 100x + 20x) cents = 125x cents.

The total monetary value given is $3.25 = 325 cents

If we take 125x = 325 we donot get the solution to be an integer

But if we take 125x = 375 we get x = 3

No.of nickels = 3, no. of quarters = 12, no. of dimes = 6