Chapter 4.2, Problem 1CYU

a.

To determine

To write an equation in standard form

Answer to Problem 1CYU

  $40x+5y=200$

Explanation of Solution

Given:

Money spent on dog kennel: $200

Charges for boarding per night: $40

Charges for walking per night: $5

Concept used:

Standard equation: $ax+by=c$

Calculation:

Let x be the number of nights for boarding and y be the number of nights for walking.

Given that the total money spent: $200

  $\Rightarrow 40x+5y=200$

Conclusion:

Therefore, the equation in standard form is $40x+5y=200.$

b.

To determine

To graph the equation in subpart (a)

Explanation of Solution

Given:

From subpart (a), $40x+5y=200.$

Calculation for graph:

  $\begin{array}{l}40x+5y=200\\ \Rightarrow 5y=200-40x\\ \Rightarrow y=\frac{200-40x}{5}\end{array}$

x	0	1	2	10	5
y	40	32	24	-40	0

Graph:

Plotting the calculated values of x and y.

  

Inference:

The equation in standard form is shown in the graph.

c.

To determine

To calculate the number of walks that could be bought

Answer to Problem 1CYU

8

Explanation of Solution

Given:

Money spent on dog kennel: $200

Charges for boarding per night: $40

Charges for walking per night: $5

From subpart (a), $40x+5y=200$

Given that the number of nights that the dog is boarded: 4

Calculation:

Let x be the number of nights for boarding and y be the number of nights for walking.

The total money spent: $200

  $\Rightarrow 40x+5y=200$

Given that the number of nights that the dog is boarded: 4

  $\begin{array}{l}\Rightarrow 40(4)+5y=200\\ \Rightarrow 160+5y=200\\ \Rightarrow 5y=40\\ \Rightarrow y=8\end{array}$

Conclusion:

Therefore, the number of walks that can be bought is 8.