You have $3.50 with twenty-seven coins, quarters, nickels, and dimes. You have three times as many dimes as nickels. Find how many of each coin you have.

Question

You have $3.50 with twenty-seven coins, quarters, nickels, and dimes. You have three times as many dimes as nickels. Find how many of each coin you have.

Answer 1

The value equation is

.10d+.05n+.25q=$3.50

 

The total number of coins is:

 

d+n+q=27

 

The last equation is:

 

d=3n

 

q=27-n-d=27-n-3n=27-4n

 

substitute these into the value equation to solve for n

 

.10(3n)+.05n+.25(27-4n)

=$3.50

 

.3n+.05n+6.75-n=3.50

3.25=.65n

n=5.  Value =$ .25

n is an integer that's good!

d=15 Value =$1.50

q=7   Value =$1.75

 

To check add the values 

Total Value =$3.50

 

And check that the number of coins sum to 27. 

Answer 2

Let # of nickels = x

Let # of dimes = 3x

Let # of quarters = y

 

We set up our equations

 

 

x + 3x + y = 27 

4x + y = 27                  eq1

 

0.05x + 0.10(3x) + 0.25y = 3.50

0.05x + 0.30x + 0.25y = 3.50

0.35x + 0.25y = 3.50                            eq2

 

 

Substitute eq1 into eq2.

 

0.35x + 0.25(27 - 4x) = 3.50

0.35x + 6.75 - x = 3.50

-0.65x = -3.25

        x = 5

 

Substitute this value into eq1.

 

y = 27 - 4x

y = 27 - 4(5)

y = 27- 20

y = 7

 

Going back to our initial variables,

 

3x = 3(5) = 15

 

 

There are 5 nickels, 15 dimes, and 7 quarters.