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) $6 \prime \prime 25 \prime \prime$ $\newline$ (B) $10 \prime \prime \times 15 \prime$ $\newline$ (C) $12 \prime \times 18 \prime$ $\newline$ (D) $15 \prime \times 18 \prime$ $\newline$ (E) None of these

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Add and subtract decimals: 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 25 \prime \prime

\newline

(B)

10 \prime \prime \times 15 \prime

\newline

(C)

12 \prime \times 18 \prime

\newline

(D)

15 \prime \times 18 \prime

\newline

(E) None of these

Determine Area Available: Determine the area available for text. Since the margins are $1$ inch on the sides and top and $2$ inches at the bottom, we need to subtract these margins from the overall dimensions of the paper to get the area available for text. Let's denote the width of the paper as $W$ and the height as $H$ . The area for text will then be $(W - 2 \times 1) \times (H - 1 - 2)$ , because we subtract $1$ inch from each side for the width and $1$ inch from the top and $2$ inches from the bottom for the height.
Set Up Equation: Set up the equation for the area available for text. The equation based on the margins is $(W - 2) \times (H - 3) = 150$ square inches. We need to find the values of $W$ and $H$ that satisfy this equation.
Check Answer Choices: Check the answer choices to see which one satisfies the equation. $\newline$ We will plug in the dimensions from each answer choice into the equation and see which one gives us an area of $150$ square inches for the text. $\newline$ (A) $6'' \times 25''$ would give us $(6 - 2) \times (25 - 3) = 4 \times 22 = 88$ square inches, which is not enough.
Correct Answer: (B) $10'' \times 15''$ would give us $(10 - 2) \times (15 - 3) = 8 \times 12 = 96$ square inches, which is also not enough.
Correct Answer: (B) $10'' \times 15''$ would give us $(10 - 2) \times (15 - 3) = 8 \times 12 = 96$ square inches, which is also not enough.(C) $12'' \times 18''$ would give us $(12 - 2) \times (18 - 3) = 10 \times 15 = 150$ square inches, which is the correct area.
Correct Answer: (B) $10'' \times 15''$ would give us $(10 - 2) \times (15 - 3) = 8 \times 12 = 96$ square inches, which is also not enough.(C) $12'' \times 18''$ would give us $(12 - 2) \times (18 - 3) = 10 \times 15 = 150$ square inches, which is the correct area.(D) $15'' \times 18''$ would give us $(15 - 2) \times (18 - 3) = 13 \times 15 = 195$ square inches, which is more than needed.
Correct Answer: (B) $10'' \times 15''$ would give us $(10 - 2) \times (15 - 3) = 8 \times 12 = 96$ square inches, which is also not enough.(C) $12'' \times 18''$ would give us $(12 - 2) \times (18 - 3) = 10 \times 15 = 150$ square inches, which is the correct area.(D) $15'' \times 18''$ would give us $(15 - 2) \times (18 - 3) = 13 \times 15 = 195$ square inches, which is more than needed.(E) None of these is not an option because we have found a correct answer in (C).