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Frank is purchasing hammers and wrenches for his workshop, and he would like to spend under $\$100$ . Each hammer costs $\$9$ , and each wrench costs $\$5$ . $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of hammers $\newline$ $y =$ the number of wrenches $\newline$ Choices: $\newline$ (A) $9x + 5y \leq 100$ $\newline$ (B) $9x - 5y \leq 100$ $\newline$ (C) 9x \times 5y < 100 $\newline$ (D) 9x + 5y < 100

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Write a linear inequality: word problems

Full solution

Q. Frank is purchasing hammers and wrenches for his workshop, and he would like to spend under

\$100

. Each hammer costs

\$9

, and each wrench costs

\$5

.

\newline

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

\newline

x =

the number of hammers

\newline

y =

the number of wrenches

\newline

Choices:

\newline

(A)

9x + 5y \leq 100

\newline

(B)

9x - 5y \leq 100

\newline

(C)

9x \times 5y < 100

\newline

(D)

9x + 5y < 100

Cost Determination: Determine the cost for each hammer and wrench. $\newline$ Cost of each hammer: $\$9$ $\newline$ Cost of each wrench: $\$5$ $\newline$ Frank wants to spend under $\$100$ .
Variable Definition: Define the variables for the number of hammers and wrenches. $\newline$ Let $x$ be the number of hammers. $\newline$ Let $y$ be the number of wrenches.
Inequality Writing: Write the inequality that represents the total cost of hammers and wrenches. $\newline$ Total cost of hammers: $9x$ (since each hammer costs $\$9$ ) $\newline$ Total cost of wrenches: $5y$ (since each wrench costs $\$5$ ) $\newline$ Frank wants to spend less than $\$100$ , so the total cost should be less than $\$100$ . $\newline$ Inequality: 9x + 5y < 100

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