Chapter 4.2, Problem 55PFA

a.

To determine

The equation in standard form

Answer to Problem 55PFA

  $0.05x+0.10y=2.25$

Explanation of Solution

Given:

The total value of money is $2.25

Calculation:

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

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

The equation in standard form is

  $0.05x+0.10y=2.25$

Conclusion:

Therefore, the equation in standard form is $0.05x+0.10y=2.25$ .

b.

To determine

To graph: the equation $0.05x+0.10y=\mathrm{2.25.}$

Explanation of Solution

Given:

  $0.05x+0.10y=2.25$

Calculation for graph:

  $\begin{array}{l}0.05x+0.10y=2.25\\ \Rightarrow 0.10y=2.25-0.05x\\ \Rightarrow y=\frac{2.25-0.05x}{0.10}\end{array}$

Substitute random values of x to find y .

x	-2	-1	0	1	2
y	23.5	23	22.5	22	21.5

Graph:

Interpretation:

The graph of given equation is plotted above.

c.

To determine

The number of dimes

Answer to Problem 55PFA

10

Explanation of Solution

Given:

Number of nickels = 25

From subpart (a),

  $0.05x+0.10y=2.25$

Calculation:

Substitute the value of x in the equation found in subpart (a).

  $\begin{array}{l}\Rightarrow 0.05x+0.10y=2.25\\ \Rightarrow 0.05(25)+0.10y=2.25\\ \Rightarrow 1.25+0.10y=2.25\\ \Rightarrow 0.10y=2.25-1.25\\ \Rightarrow 0.10y=1\\ \Rightarrow y=10\end{array}$

Conclusion:

Therefore, the number of dimes in 10.