Translate the sentence to an algebraic inequality.
-Assume that the mathematical model $\mathrm { C } ( \mathrm { x } ) = 16 \mathrm { x } + 140$ represents the cost $\mathrm { C }$, in hundreds of dollars, for a certain manufacturer to produce $x$ items. How many items $x$ can be manufactured while keeping costs between between $\$ 526,000$ and $\$ 782,000$ ?
A) $320

Question

Translate the sentence to an algebraic inequality.
-Assume that the mathematical model $\mathrm { C } ( \mathrm { x } ) = 16 \mathrm { x } + 140$ represents the cost $\mathrm { C }$, in hundreds of dollars, for a certain manufacturer to produce $x$ items. How many items $x$ can be manufactured while keeping costs between between $\$ 526,000$ and $\$ 782,000$ ?
A) $320 < x < 480$
B) $480 < \mathrm { x } < 640$
C) $340 < x < 510$
D) $510 < x < 680$

Quizplus · Accepted Answer

Given the cost model $C(x) = 16x + 140$, where $C$ is in hundreds of dollars, to find the range of $x$ for costs between \$526,000 and \$782,000, we convert these values to hundreds of dollars (\$526,000 becomes 5260 and \$782,000 becomes 7820) and solve the inequalities $5260 \leq 16x + 140 \leq 7820$. Simplifying these inequalities gives the range for $x$ as $320 < x < 480$.

Translate the Sentence to an Algebraic Inequality C(x)=16x+140\mathrm { C } ( \mathrm { x } ) = 16 \mathrm { x } + 140C(x)=16x+140

Translate the Sentence to an Algebraic Inequality $\mathrm { C } ( \mathrm { x } ) = 16 \mathrm { x } + 140$