Chapter 3, Problem 2CR

To determine

To Calculate:The possibility for number of dimes.

Answer to Problem 2CR

According to equation, option $\left(c\right)$ is correct answer.

Explanation of Solution

Given Information:In this question, dimes and quarters cost is given to check all possibility for number of dimes.

Concept Used:

Following steps must be taken to simplify equation.

Step $1$ : First we have to design equation in terms of dimes and quarters

Step $2$ : Solve equation to get all possibility for number of dimes.

Calculation:

Assume that Frank has $x$ dimes and $y$ quarters.

As per the above-mentioned concept,

  $0.10x+0.25y=1.85\Rightarrow 20(0.10x+0.25y)=20(1.85)$ .

  $\Rightarrow 2x+5y=37$ , Solve for $x$ in terms of $y$ .

  $\Rightarrow x=\frac{37-5y}{2}$   $\left(1\right)$

  $37-5y$ Always be even so $y$ will be odd.

Then $y=\left(1,3,5,7\right)$ .

Put $y$ value in equation $\left(1\right)$ , $x=\left(16,11,6,1\right)$ .

All possibility of number of dimes are $x=\left(1,6,11,16\right)$ .

Option $\left(c\right)$ is correct answer.