SOLUTION: A bag has 274 coins of nickels, dimes and quarters. There are twice as many nickels as quarters. If the total value of the coins was $30.3, how many nickels, dimes and quarters wer

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Question 1196588: A bag has 274 coins of nickels, dimes and quarters. There are twice as many nickels as quarters. If the total value of the coins was $30.3, how many nickels, dimes and quarters were there?
Found 3 solutions by ikleyn, josgarithmetic, MathTherapy:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

x quarters;

2x nickels,

and (274-x-2x) = (274-3x) dimes.


Total money equation is

    25x + 5*(2x) + 10*(274-3x) = 3030  cents.


Simplify and solve

    25x + 10x + 2740 - 30x = 3030

          5x               = 3030 - 2740 = 290

           x                             = 290/5 = 58.


ANSWER.  58 quarters;  2*58 = 116 nickels and the rest coins, 274-58-116 = 100, are dimes.


CHECK.   25*58 + 5*116 + 10*100 = 3030 cents, in total.  ! Correct !

Solved.

The lesson to learn

        this problem is to solve using one equation in one single unknown.



Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
COIN          COIN COUNTS          MONEY(dollars)
Nickels       2Q                   0.05*2Q
Dimes        274-2Q-Q=274-3Q       0.1*(274-3Q)
Quarters       Q                   0.25Q
TOTAL                             30.30

0.05%2A2Q%2B0.1%28274-3Q%29%2B0.25Q=30.30
-
0.1Q%2B0.1%28274-3Q%29%2B0.25Q=30.30
10Q%2B10%28274-3Q%29%2B25Q=3030
10Q%2B2740-30Q%2B25Q=3030
5Q%2B2740=3030
5Q=3030-2740=290
Q=290%2F5
highlight%28Q=58%29 and counts for nickels and dimes are easily found.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

A bag has 274 coins of nickels, dimes and quarters. There are twice as many nickels as quarters. If the total value of the coins was $30.3, how many nickels, dimes and quarters were there?
Let number of quarters be Q
Then number of nickels = 2Q
Also, number of dimes = 274 - Q - 2Q = 274 - 3Q

We then get the following VALUE equation: .25Q + .05(2Q) + .1(274 - 3Q) = 30.3
.25Q + .1Q + 27.4 - .3Q = 30.3
.25Q + .1Q - .3Q = 30.3 - 27.4
.05Q = 2.9
Number of quarters or 

Number of nickels: 2(58) = 116   

Number of dimes: 274 - 3(58) = 274 - 174 = 100