The total weekly sales for a newly released portable media player (PMP)increased each week.At the same time,the total weekly sales for another newly released PMP decreased each week.Models that approximate the total weekly sales S (in thousands of units)for each PMP are $$\left\{ \begin{array} { l l }
S = 10 x + 70 & \text { PMP1 } \
S = - 10 x + 210 & \text { PMP2 }
\end{array} \right.$$ where x represents the number of weeks each PMP was in stores,with x = 0 corresponding to the PMP sales on the day each PMP was first released in stores.After how many weeks will the sales for the two PMPs be equal?

A)11 weeks
B)9 weeks
C)7 weeks
D)3 weeks
E)5 weeks

Question

The total weekly sales for a newly released portable media player (PMP)increased each week.At the same time,the total weekly sales for another newly released PMP decreased each week.Models that approximate the total weekly sales S (in thousands of units)for each PMP are​ $$\left\{ \begin{array} { l l } 
S = 10 x + 70 & \text { PMP1 } \
S = - 10 x + 210 & \text { PMP2 }
\end{array} \right.$$ ​ where x represents the number of weeks each PMP was in stores,with x = 0 corresponding to the PMP sales on the day each PMP was first released in stores.After how many weeks will the sales for the two PMPs be equal?
​
A)11 weeks
B)9 weeks
C)7 weeks
D)3 weeks
E)5 weeks

Quizplus · Accepted Answer

To find when the two PMPs will have equal sales, we need to set their respective sales equations equal to each other and solve for x:

150 + 6x = 300 - 12x

18x = 150

x ≈ 8.33

Since we're dealing with whole weeks, we round down to the nearest week and get x = 8. Thus, it will take 8 weeks for the two PMPs to have equal sales. However, we need to add 1 week to account for the first week of sales (when x = 0), so the total time is 9 weeks. Therefore, the answer is B) 7 weeks.

The Total Weekly Sales for a Newly Released Portable Media {S=10x+70 PMP1 S=−10x+210 PMP2 \left\{ \begin{array} { l l } S = 10 x + 70 & \text { PMP1 } \\S = - 10 x + 210 & \text { PMP2 }\end{array} \right.{S=10x+70S=−10x+210​ PMP1 PMP2 ​

The Total Weekly Sales for a Newly Released Portable Media $\left\{ \begin{array} { l l } S = 10 x + 70 & \text { PMP1 } \\S = - 10 x + 210 & \text { PMP2 }\end{array} \right.$