A piece of paper is to display $150$ square inches of text. If there are to be one-inch margins on the sides and the top and a two-inch margin at the bottom, what are the dimensions of the smallest piece of paper that can be used? $\newline$ Choose $1$ answer: $\newline$ (A) $6 \prime \prime \times 25 \prime \prime$ $\newline$ (B) $10 \prime \prime \times 15 \prime \prime$ $\newline$ (C) $12 \prime \prime \times 18 \prime \prime$ $\newline$ (D) $15 \prime \prime \times 18 \prime \prime$ $\newline$ (E) None of these

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Solve linear equations with variables on both sides: word problems

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Q. A piece of paper is to display

150

square inches of text. If there are to be one-inch margins on the sides and the top and a two-inch margin at the bottom, what are the dimensions of the smallest piece of paper that can be used?

\newline

Choose

1

answer:

\newline

(A)

6 \prime \prime \times 25 \prime \prime

\newline

(B)

10 \prime \prime \times 15 \prime \prime

\newline

(C)

12 \prime \prime \times 18 \prime \prime

\newline

(D)

15 \prime \prime \times 18 \prime \prime

\newline

(E) None of these

Define Variables: Let's call the width of the paper $w$ inches and the height $h$ inches. The text area is $150$ square inches.
Calculate Text Area: The margins reduce the width by $2$ inches ( $1$ inch on each side) and the height by $3$ inches ( $1$ inch on the top and $2$ inches at the bottom).
Solve Equation: So, the text area can be represented by $(w - 2)(h - 3) = 150$ .
Evaluate Options: We need to find the smallest $w$ and $h$ that satisfy this equation. Let's start by trying the options given.
Option A: Option (A): If $w = 6$ and $h = 25$ , then $(6 - 2)(25 - 3) = 4 \times 22 = 88$ , which is not equal to $150$ .
Option B: Option (B): If $w = 10$ and $h = 15$ , then $(10 - 2)(15 - 3) = 8 \times 12 = 96$ , which is not equal to $150$ .
Option C: Option (C): If $w = 12$ and $h = 18$ , then $(12 - 2)(18 - 3) = 10 \times 15 = 150$ , which is equal to $150$ .
Final Dimensions: So, the dimensions of the smallest piece of paper that can be used are $12$ inches by $18$ inches.