Chapter 6.4, Problem 15MCQ

To determine

To find the number of nickels and dimes if the total value is $1.70 and total coins are 21.

Answer to Problem 15MCQ

8 nickels and 13 dimes.

Explanation of Solution

Given information:

Total coins are 21 and total value is $1.70

Calculation:

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

Then,

  $\begin{array}{l}x+y=21\to \left(1\right)\left[\text{Total}\text{coins}\right]\\ 0.05x+0.1y=1.70\to \left(2\right)\left[\text{Total}\text{value}\right]\end{array}$

Now,

  $\begin{array}{l}\left[0.05\times \text{Equation}\left(\text{1}\right)\right]-\left[\text{Equation}\left(\text{2}\right)\right]\\ \Rightarrow 0.05\left(x+y\right)-\left(0.05x+0.1y\right)=0.05\left(21\right)-1.70\\ \Rightarrow 0.05x+0.05y-0.05x-0.1y=1.05-1.70\\ \Rightarrow -0.05y=-0.65\\ \Rightarrow y=13\end{array}$

Now put $y=13$ in equation (1), we get

  $\begin{array}{l}x+13=21\\ \Rightarrow x=8\end{array}$

Therefore there are 8 nickels and 13 dimes.