Respuesta :
Solution
Coach A:
- This coach charges $5,000 initial fee and $450 per month. This implies that:
[tex]\begin{gathered} \text{ At the point of hire,} \\ C=\$5000 \\ \\ \text{ After 1 month,} \\ C=\$5000+\$450 \\ \\ \text{ After 2 months,} \\ C=\$5000+2(\$450) \\ \\ ... \\ \text{ After n months,} \\ C=\$5000+n(\$450) \end{gathered}[/tex]Coach B:
- This coach charges $4000 inital fee and $700 per month. This implies that:
[tex]\begin{gathered} \text{ At point of hire,} \\ C=\$4000 \\ \\ \text{ After 1 month,} \\ C=\$4000+\$700 \\ \\ \text{ After 2 months,} \\ C=\$4000+2(\$700) \\ \\ ... \\ \text{ After n months,} \\ C=\$4000+n(\$700) \end{gathered}[/tex]- When the two coaches charge the same amount of money, the cost functions of both coaches should be equated.
- Thus, we have:
[tex]\begin{gathered} 4000+n(700)=5000+n(450) \\ 4000+700n=5000+450n \\ \text{ Subtract 450n and 4000 from both sides} \\ \\ 700n-450n=5000-4000 \\ 250n=1000 \\ \\ \text{ Divide both sides by 250} \\ \\ \frac{250n}{250}=\frac{1000}{250} \\ \\ \therefore n=4 \end{gathered}[/tex]Final Answer
The two coaches charge the same amount by the 4th month
