Question

Jimmy has been collecting nickels and quarters.His coin collection consists of 154 coins.The total value of his coin collection is $18.90.

Answer 1

Step 1:

Use the concept below

A nickel is worth 5 cents. A dime is worth 10 cents. A quarter is worth 25 cents.

Let the number of nickel = n

Let the number of quarters = q

Step 2:

You will have to convert cent to the dollar because the total value of coin collection is in dollars.

5 cents = $0.05

25 cents = $0.25

Step 3:

The total number of coins = 154

`\begin{gathered} \text{n + q = 154} \\ 0.05n\text{ + 0.25q = 18.9} \end{gathered}`

Step 4:

Solve the systems of equations to find the values of n and q.

From the first equation, make n the subject of the formula and substitute in the equation 2.

`\begin{gathered} \text{n = 154 - q} \\ 0.05n\text{ + 0.25q = 18.9} \\ 0.05(154\text{ - q) + 0.25q = 18.9} \\ 7.7\text{ - 0.05q + 0.25q = 18.9} \\ 0.2q\text{ = 18.9 - 7.7} \\ 0.2q\text{ = 11.2} \\ q\text{ = }(11.2)/(0.2) \\ q\text{ = 56} \end{gathered}`

Step 5:

`\begin{gathered} n\text{ = 154 - q} \\ \text{n = 154 - 56} \\ \text{n = 98} \end{gathered}`

Final answer

98 nickels

56 quarters