Question

Use the 4 step process to answer this word problem: Assign and label variables, write a system of equations, solve the system, answer the question in a sentence. In your coin purse are dimes and quarters, 50 coins in all. The total value of the coins is $9.95. How many of each coin do you have?

Answer 1

Answer: There are 33 dimes and 17 quarters in my pocket.

Explanation:

Step 1: To assign and label the variables.

Suppose,

The number of dimes= x

The number of quarters= y

Step 2: To write the system of equations.

Equation related to the total coins:

x + y = 50 equation 1

Equation related to the total value of the coins:

0.10x + 0.25y = 9.95 equation 2

Step 3: To solve the system of equations.

Multiply equation 1 by 0.10 and then subtract it from equation 2 to eliminate the variable, x.

0.10x + 0.25y – (0.10x + 0.10y)= 9.95 – 5

0.15y = 4.95

y= 33

So, x=50 - 33= 17

Step 4: Therefore, there are 33 dimes and 17 quarters in my pocket.