Chapter 6.2, Problem 35PFA

To determine

To find: System of equations.

Answer to Problem 35PFA

Option D

  $\begin{array}{l}5n+10d=185\\ n-d=1\end{array}$

Explanation of Solution

Given information:

Value of collection of nickels and dimes = $1.85

Value of dimes = 2(value of dimes) − 0.10

Let $n$ be number of nickels and $d$ be the number of dimes.

we know

value of 1 dime = $\$0.10$

value of 1 nickel = $\$0.05$

Total value of collection = number of nickels $\times$ value of each nickel + number of dimes $\times$ value of each dime

  $\Rightarrow 1.85=0.05n+0.10d$

Multiplying with 100 on both sides

We get

  $\begin{array}{l}\Rightarrow 100\left(0.05n\right)+100\left(0.10d\right)=1.85\times 100\\ \Rightarrow 5n+10d=185\end{array}$

  $5n+10d=185$ ------------------(1)

Given

Value of dimes =2(value of nickels) − 0.10

  $\begin{array}{l}\Rightarrow 0.10d=2\left(0.05n\right)-0.10\\ \Rightarrow 0.10d=0.10n-0.10\end{array}$

Multiplying with 100 on both sides

We get

  $\begin{array}{l}\Rightarrow 0.10d=2\left(0.05n\right)-0.10\\ \Rightarrow 100\left(0.10d\right)=100\left(0.10n\right)-100\left(0.10\right)\\ \Rightarrow d=n-1\\ \Rightarrow n-d=1\end{array}$

  $n-d=1$ ---------(2)

Equations (1) and (2) are the system of equations that are required to find the number of nickels and dimes.

  $\begin{array}{l}5n+10d=185\\ n-d=1\end{array}$