Question

The equation below model the numbers of two portable music players (y) and days after both players were introduced (x).

Music player A: y=191x-32 and music player B: y=-x^2+200x+20
1.on what day(s) did the company sell the same number of each player ?
2.how many players were sold on THAT day (use your answer from #1)

Answer 1

a. On the 13th day

b. 2,451 players we’re sold on that day

Explanation:

a. The day in which the company sold the same number of players can be calculated by equating the values of y that we have ;

y = 191x-32 and y = -x^2 + 200x + 20

Equating both, we have;

191x-32 = -x^2 + 200x + 20

x^2 -200x + 191x-20-32 = 0

x^2-9x-52 = 0

x^2-13x + 4x -52 = 0

x(x-13)+4(x-13) = 0

(x-13)(x+4) = 0

x = 13 or -4

as days cannot be negative we choose only x = 13

This means the company sold equal numbers of players on the 13th day

b. To get the number of players sold on that day, we choose any of the y equation and substitute x = 13

Thus, we have for y = 191x -32; 191(13) - 32 = 2,451 players