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Celine is fixing up her home and must spend less than $\$7,200$ to hire carpenters and painters. Carpenters charge $\$43$ per hour and painters charge $\$35$ per hour. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of hours of carpentry $\newline$ $y =$ the number of hours of painting $\newline$ $\newline$ Choices: $\newline$ (A) $43x + 35y \geq 7,200$ $\newline$ (B) 43x + 35y < 7,200 $\newline$ (C) 43x + 35y > 7,200 $\newline$ (D) $43x + 35y \leq 7,200$

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Write a linear inequality: word problems

Full solution

Q. Celine is fixing up her home and must spend less than

\$7,200

to hire carpenters and painters. Carpenters charge

\$43

per hour and painters charge

\$35

per hour.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of hours of carpentry

\newline

y =

the number of hours of painting

\newline

\newline

Choices:

\newline

(A)

43x + 35y \geq 7,200

\newline

(B)

43x + 35y < 7,200

\newline

(C)

43x + 35y > 7,200

\newline

(D)

43x + 35y \leq 7,200

Calculate Carpentry Cost: Determine the cost for carpentry services. $\newline$ Celine needs to hire carpenters at a rate of $\$43$ per hour. If she hires them for $x$ hours, the total cost for carpentry will be: $\newline$ Cost of carpentry = Hourly rate of carpenters $\times$ Number of hours of carpentry $\newline$ = $\$43 \times x$ $\newline$ = $43x$
Calculate Painting Cost: Determine the cost for painting services. $\newline$ Celine needs to hire painters at a rate of $\$35$ per hour. If she hires them for $y$ hours, the total cost for painting will be: $\newline$ Cost of painting = Hourly rate of painters $\times$ Number of hours of painting $\newline$ = $\$35 \times y$ $\newline$ = $35y$
Form Inequality: Combine the costs to form an inequality. $\newline$ Celine's total spending on carpentry and painting must be less than $\$7,200$ . The combined cost is the sum of the cost of carpentry and the cost of painting: $\newline$ Total cost = Cost of carpentry + Cost of painting $\newline$ = $43x + 35y$ $\newline$ The inequality that represents this situation is: $\newline$ 43x + 35y < 7,200

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