A jar contains nickels and pennies. There are 56 coins in the jar in all. The total value of the coins is $1.52. How many pennies are in the jar?

Answer 1

Let’s use n to represent the number of nickels in the jar, and p to represent the number of pennies in the jar.

Step 1:

Let’s start by considering the number of coins we have. We know there are 56 coins in the jar. In other words, the number of pennies plus the number of nickels equals 56.

p + n = 56

Step 2:

Let’s now consider the value of the coins. We know that the total value of coins in the jar is $1.52. We also know that nickels are $0.05, and pennies are $0.01. Given this information, we can make the following statement:

(.01) * (# of pennies) + (.05) * (# of nickels) = 1.52

or

.01p + .05n = 1.52

So now we have two equations:

p + n = 56

.01p + .05n = 1.52

Step 3:

We can use substitution to solve these two equations.

3a:

Rearrange the first equation so that only one variable is on the left by subtracting p from both

sides of the equation:

p + n = 56

-p = -p

——————

n = 56 - p

3b: substitute this equation into the second.

.01p + .05 ( n ) = 1.52

.01p + .05 ( 56 - p) = 1.52

3c: solve for p:

Multiply (.05) by (56 - p), and now we have:

.01p + 2.8 - .05p = 1.52

Combine like terms:

2.8 -.04p = 1.52

Subtract 2.8 from both sides of the equation:

2.8 -.04p = 1.52

-2.8 -2.8

———————-

-.04p = -1.28

Divide both sides of the equation by -.04:

p = 32

Step 4: use the first equation to solve for n:

n + p = 56

n + 32 = 56

n = 24

32 pennies and 24 nickels = $1.52.