Chapter 6.5, Problem 29PFA

To determine

To calculate the number of dimes and nickels in Erin’s pocket.

Answer to Problem 29PFA

Dimes:12

Nickels:18

Explanation of Solution

Given:

The total number of coins Erin has: 30

Value of the change in her pocket: $2.10

Calculation:

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

Given that there are 30 coins in total.

  $\Rightarrow x+y=\mathrm{30.............................}(1)$

The total value of the coins she has is $2.10

The value of one nickel is $0.05 and the value of one dime is $0.10.

  $\Rightarrow 0.10x+0.05y=\mathrm{2.10......................}(2)$

From equation (1),

  $\Rightarrow x=30-y\mathrm{.............................}(3)$

Substitute equation (3) in equation (2).

  $\begin{array}{l}\Rightarrow 0.10(30-y)+0.05y=2.10\\ \Rightarrow 3-0.10y+0.05y=2.10\\ \Rightarrow -0.05y=2.10-3\\ \Rightarrow -0.05y=-0.9\\ \Rightarrow y=18\end{array}$

Substitute the value of y in equation (1).

  $\begin{array}{l}\Rightarrow x+18=30\\ \Rightarrow x=30-18\\ \Rightarrow x=12\end{array}$

Conclusion:

Therefore, the number of dimes is 12 and the number of nickels is 18.