Soccer balls go on sale for $7.50 each. The store also sells footballs and the manager wants to earn a daily profit of $400 from
both items. The equation y=-4x^2+80x-150 models the store’s daily profit, y, for selling footballs at x dollars. Explain how to find the price per football needed to meet the goal.
At $7.50 per soccer ball, they earn a daily profit of $232.50. The store needs to earn a daily profit of $400 – $232.50 = $167.50 from footballs. Solve 167.50 = –4x2 + 80x – 150 to find the price for footballs: x = $5.46 and $14.54.
Using the information that we have about the soccer ball prices, we can find out their daily profit to see how much the footballs daily profit should be. Plugging in 7.50 into the equation, we get 232.5 as their daily profit. To find what the footballs daily profit should be, we must minus 232.5 from 400. This ends up with 167.5
Now to find the price of the footballs, we must plug 167.5 into the equation and use the quadratic formula to find the prices.
