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It takes $31$ employees and $ext{ extdollar}7500$ to build a car, and it takes $19$ employees and $ext{ extdollar}4300$ to build a motorcycle. Genghis Motors wants to spend more than $ext{ extdollar}84000$ to build cars and motorbikes using at most $706$ employees. Let $C$ denote the number of cars they build and $M$ the number of motorbikes they build. Write an inequality that represents the condition based on the number of employees.

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One-step inequalities: word problems

Full solution

Q. It takes

31

employees and

ext{ extdollar}7500

to build a car, and it takes

19

employees and

ext{ extdollar}4300

to build a motorcycle. Genghis Motors wants to spend more than

ext{ extdollar}84000

to build cars and motorbikes using at most

706

employees. Let

C

denote the number of cars they build and

M

the number of motorbikes they build. Write an inequality that represents the condition based on the number of employees.

Given Information: We know it takes $31$ employees to build a car and $19$ employees to build a motorcycle.
Variables Defined: Let $C$ be the number of cars and $M$ be the number of motorbikes.
Total Employees Calculation: The total number of employees used is $31C + 19M$ .
Constraint Inequality: Genghis Motors wants to use at most $706$ employees.
Maximum Employees Limit: So, the inequality is $31C + 19M \leq 706$ .

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