Solve the problem.
-The revenue achieved by selling $x$ graphing calculators is figured to be $x ( 28 - 0.2 x )$ dollars. The cost of each calculator is $\$ 20$. How many graphing calculators must be sold to make a profit (revenue - cost) of at least $\$ 75.00 ?$
A) $\{ x \mid 17

Question

Solve the problem.
-The revenue achieved by selling $x$ graphing calculators is figured to be $x ( 28 - 0.2 x )$ dollars. The cost of each calculator is $\$ 20$. How many graphing calculators must be sold to make a profit (revenue - cost) of at least $\$ 75.00 ?$
A) $\{ x \mid 17 < x < 23 \}$
B) $\{ x \mid 16 < \mathrm { x } < 14 \}$
C) $\{ x b 5 < x < 15 \}$
D) $\{ x \mid 15 < x < 25 \}$

Quizplus · Accepted Answer

To find the number of calculators $x$ that must be sold to make a profit of at least $75, we first express the profit equation: Profit = Revenue - Cost = $x(28 - 0.2x) - 20x$. Simplifying this gives us the quadratic equation in terms of profit. Setting the profit to be at least $75 and solving for $x$ will give us the range of $x$ that satisfies this condition. The correct range that results from solving this equation is $15 < x < 25$, which corresponds to choice D.

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