A collection of dimes, nickels and quarters amounts to $11.95. If there are 173 coins in all and there are twice as many dimes as there are quarters, find the number of nickels.

1) Write down all of the variables:

dimes = d

nickels=n

quarters=q

Then write down the facts.

d=2q (there are twice as many dimes as quarters)

d+n+q=173 (there are 173 coins in all)

d(.1)+n(.05)+q(.25) = 11.95 (the dimes, nickels and quarters amounts to $11.95)

There are three separate equations and three variables. You can solve them as a system of equations. It is probably simplest to use substitution.

for:

d+n+q=173

We already know that d=2q so we can substitute 2q for d in the second equation.

2q+n+q=173

you can simplify this to

n=173-3q

Now we have substitutions for 2 of the three variable that can be plugged into the third equation.

2q=d

n=173-3q

for

d(.1)+n(.05)+q(.25) = 11.95

substitution yeilds

2q(.1)+(173-3q)(.05)+q(.25)=11.95

multiply both sides of the equation by 100 to eliminate the decimal.

20q+(173-3q)(5)+q(25)=1195

20q+(865-15q)+q(25)=1195

30q+865=1195

30q=330

q = 11

now take your value for q and find the values of n and d

d=2q

d=2(11)

d=22

d+n+q=173

22+n+11=173

n=140

number of dimes=22

number of quarters=11

number of nickels=140

substitute these figures into the last equation to check your answer

d(.1)+n(.05)+q(.25) = 11.95

22(.1)+140(.05)+11(.25)=11.95

2.2+7+2.75=11.95

11.95=11.95

We can reasonably assume that we are correct in saying that there are 140 nickels.