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
[tex]\begin{gathered} \text{n + q = 154} \\ 0.05n\text{ + 0.25q = 18.9} \end{gathered}[/tex]
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.
[tex]\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{ = }\frac{11.2}{0.2} \\ q\text{ = 56} \end{gathered}[/tex]
Step 5:
[tex]\begin{gathered} n\text{ = 154 - q} \\ \text{n = 154 - 56} \\ \text{n = 98} \end{gathered}[/tex]
Final answer
98 nickels
56 quarters
