Question

The equations y = 30x + 10 and y = –x2 + 150x + 10 model the daily sales of two car models, where x represents the number of days since the cars went on sale. On what day was the same number of each car sold?

Answer 1

Both equations should be equal

• 30x+10=-x²+150x+10
• 30x=-x²+150x
• -120x=-x²
• x²=120x
• x=120 or 0

So the days are 0 and 120

Answer 2

day 0, day 120

Explanation:

You want to find the value of x that makes both y-values be the same:

y = y

30x +10 = -x^2 +150x +10

x^2-120x = 0 . . . . subtract the right side of the equation

x(x -120) = 0 . . . . . factor

Values of x that make this true are x=0 and x=120.

The same number of each car was sold on day 0 and day 120.