Chapter 1, Problem 7CA

(a)

To determine

Towrite: The equation for the expenses of the TV services when the person and person’s friend paid same amount and then solve the equation.

Answer to Problem 7CA

The equation for the expenses of the TV services when the person and person’s friend paid same amount is $45x=36x+99$ and the number of months is $x=11$ .

Explanation of Solution

Given:

For cable TV the person have to pay $\$45$ per month and the person’s friend have to pay $\$99$ for the additional amount to buy satellite TV receiver and then have to pay monthly charge $\$36$ .

Consider $x$ be the no of months.

The charge for cable TV by the person is $45x$ .

The charge for satellite TV by the person is $36x+99$ .

The equation when the person and person’s friend pay the same amount for TV is as follows:

$\begin{array}{l}45x=36x+99\\ 45x-36x=99\\ 9x=99\\ x=\frac{99}{9}\\ x=11\end{array}$

Therefore, the person and person’s friend will pay the same amount after $11$ months.

Conclusion:

Thus, the equation for the expenses of the TV services when the person and person’s friend pay same amount is $45x=36x+99$ and the number of months is $x=11$ .

(b)

To determine

To check: Whether the statement of person’s friend is correct or not and explain with reasoning.

Answer to Problem 7CA

Yes, the person’s friend is correct.

Explanation of Solution

Calculation:

The yearly TV expenses of the person is as follows:

$\$45\cdot 12=\$540$

The yearly TV expenses of the person’s friend is as follows:

$\$99+\$36\cdot 12=\$531$

Therefore, the person’s friend is correct.

Conclusion:

Thus, the person’s friend is correct.