SOLUTION: A piggy bank contains only quarters and nickels, and there is a total of 60 coins. The value of coins in the piggy bank is $7.40. How many quarters are in the piggy bank?

Hi, there--

The Problem:
A piggy bank contains only quarters and nickels, and there is a total of 60 coins. The value of coins in
the piggy bank is $7.40. How many quarters are in the piggy bank?

A Solution:
Let q be the number of quarters.
Let n be the number  of nickels.

Now we need to write two equations using the information in the problem.

There is a total of 60 coins. In other words,
[the number of quarters] + [the number of nickels] = [the total number of coins]
In algebra , we write this relationship as
q + n = 60

The value of the coins in the piggy bank is $7.40. In other words,
[the value of the quarters] + [the value of the nickels] = [$7.40]
The value of the quarters is 0.25 times the number of quarters, or 0.25q.
The value of the nickels is 0.05 times the number of nickels, or 0.05n.
In algebra, we write
0.25q + 0.05n = 7.40

Now we have a system of equations with two variables. We will use the substitution method 
to solve for q and n.

Rearrange the first equation to a "q=" form. (Subtract n from both sides of the equation.
q + n = 60
q = 60 - n

We see that q and 60-n are equivalent. Substitute 60-n for q in the second equation.
0.25q + 0.05n = 7.40
0.25(60-n) + 0.05n = 7.40

Simplify and solve for n. Clear the parentheses.
15 - 0.25n + 0.05n = 7.40

Combine like terms.
15 - 0.20n = 7.40

Subtract 15 from both sides of the equation.
-0.20n = 7.40 - 15
-0.20n = -7.60

Divid both sides of the equation by -0.20.
n = -7.60/-0.20
n = 38.

There are 38 nickels. Since there are 60 coins altogether, there must be 60-38=22 quarters.

We need to check this number of each coin adds up to $7.40.
38 nickels is 38*0.05 = $1.90
22 quarters is 22*0.25 = $5.50
$1.90+5.50 = $7.40.

Everything checks out; there are 22 quarters.

Feel free to email me if you have questions about the solution.

Ms.Figgy
math.in.the.vortex@gmail.com