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.

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Mathematics

25 June, 02:27

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.

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Thomas Archer · Answer 1

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.