Chapter 6, Problem 51SGR

To determine

To write a system of equations to calculate the number of dimes and quarters.

Answer to Problem 51SGR

Number of quarters: 10

Number of dimes: 15

Explanation of Solution

Given:

Value of 25 coins both dimes and quarter is $4.00.

Concept used:

Assume separate variables for each object. Form two equations with the variables. Use elimination method and solve the system of equations.

Calculation:

Let x be the number of quarters and y be the number of dimes.

We know that the value of a quarter is $0.25 and the value of a dime is $0.10.

The total number of coins in the piggy bank is 25.

  $\Rightarrow x+y=25$   ......... (1)

The value of 25 coins is $4.00 while the value of dime is $0.10 and the value of quarter is $0.25

  $\Rightarrow 0.25x+0.10y=4.00$   ...... (2)

Multiplying (2) with 4,

  $\Rightarrow x+0.40y=16$   ......... (3)

Subtracting (3) from (1),

  $\begin{array}{l}x+y=25\\ \frac{-x-0.40y=-16}{0.6y=9}\end{array}$

Dividing 0.6 on both sides,

  $\begin{array}{c}\frac{0.6y}{0.6}=\frac{9}{0.6}\\ y=\frac{9\times 10}{0.6\times 10}\\ y=\frac{90}{6}\\ y=15\end{array}$

Substituting the value of y in (1),

  $x+15=25$

Substituting 15 on both sides,

  $\begin{array}{c}x+15-15=25-15\\ x=10\end{array}$

Conclusion:

The piggy bank has 10 quarters and 15 dimes.