SOLUTION: A coin bank contains 25 coins in nickels, dimes and quarters. There are four times as many dimes as quarters. The value of the coins is $2.05. How many dimes are in the bank?

Algebra ->  Human-and-algebraic-language -> SOLUTION: A coin bank contains 25 coins in nickels, dimes and quarters. There are four times as many dimes as quarters. The value of the coins is $2.05. How many dimes are in the bank?      Log On


   

Question 894546: A coin bank contains 25 coins in nickels, dimes and quarters. There are four times as many dimes as quarters. The value of the coins is $2.05. How many dimes are in the bank?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
n%2Bd%2Bq=25, d%2Fq=3, 0.05n%2B0.10d%2B0.25q=2.05.

Adjust the ratio equation into d=3q.

Multiply the money account equation by 20:
n%2B2d%2B5q=41.

Interesting you are asked for the number of dimes, d. You have this system of equations:
highlight_green%28system%28n%2Bd%2Bq=25%2Cd=3q%2Cn%2B2d%2B5q=41%29%29.

Do you know what to do to solve this system?

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A coin bank contains 25 coins in nickels, dimes and quarters. There are four times as many dimes as quarters. The value of the coins is $2.05. How many dimes are in the bank?


Let number of nickels, dimes, and quarters, be N, D, and Q, respectively

Then: N + D + Q = 25 ---- eq (i)

Also, D = 4Q ------- eq (ii)

N + 4Q + Q = 25 ---- Substituting 4Q for D in eq (i)

N + 5Q = 25 -------- eq (iii)

Also, .05N + .1(4Q) + .25(Q) = 2.05

.05N + .4Q + .25Q = 2.05

  .05N + .65Q =   2.05 ------ eq (iv)

- .05N - .25Q = - 1.25 ------ Multiplying eq (iii) by - .05 ---- eq (v)

          .4Q =     .8 ------ Adding eqs (v) & (iv)

Q, or number of quarters = .8%2F.4, or 2

Number of dimes: 4(2), or highlight_green%28highlight_green%288%29%29

You can do the check!! 



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