Solve the problem.
-The revenue achieved by selling x graphing calculators is figured to be x(50 - 0.5x) dollars. The cost of each calculator is $14. How many graphing calculators must be sold to make a profit (revenue - cost) of at least
$630.00?
A) $\{ x \mid 32

Question

Solve the problem.
-The revenue achieved by selling x graphing calculators is figured to be x(50 - 0.5x) dollars. The cost of each calculator is $14. How many graphing calculators must be sold to make a profit (revenue - cost) of at least
$630.00? 
A) $\{ x \mid 32 < x < 40 \}$
B) $\{ x \mid 30 < x < 42 \}$
C) $\{ \mathrm { x } \mid 39 < \mathrm { x } < 51 \}$
D) $\{ x \mid 31 < x < 41 \}$

Quizplus · Accepted Answer

To find the number of calculators, x, that must be sold to make a profit of at least $630, we first express the profit equation: Profit = Revenue - Cost. The revenue from selling x calculators is given by $x(50 - 0.5x)$, and the cost is $14 per calculator, so the cost is $14x$. Thus, the profit equation is $x(50 - 0.5x) - 14x \geq 630$. Simplifying, we get $36x - 0.5x^2 \geq 630$. Rearranging, $0.5x^2 - 36x + 630 \leq 0$. Solving this quadratic inequality, we find the range of x that satisfies the condition. The correct range that results in a profit of at least $630 is $30 < x < 42$, which corresponds to choice B.

Solve the Problem {x∣32<x<40}\{ x \mid 32 < x < 40 \}{x∣32<x<40}

Solve the Problem $\{ x \mid 32 < x < 40 \}$