Question

A postage stamp is being designed with a height of 112
inches. The area must be no greater than 118 in.2
. What is the solution to an inequality that describes the possible width of the stamp?(1 point)
Responses

w≤34 in.
w less-than-or-equal-to Start Fraction 3 over 4 End Fraction in.

w≤38 in.
w less-than-or-equal-to Start Fraction 3 over 8 End Fraction in.

w≤258 in.
w less-than-or-equal-to 2 Start Fraction 5 over 8 End Fraction in.

w<34 in.

Answer 1

To solve the problem, let's set up the inequality based on the dimensions given for the postage stamp:

Given:
- Height \( h = 112 \) inches
- Area \( A \leq 118 \) in²

The area of a rectangle is given by the formula:

\[
A = \text{height} \times \text{width}
\]

Substituting the known values:

\[
112 \times w \leq 118
\]

Next, we will divide both sides of the inequality by 112 to solve for \( w \):

\[
w \leq \frac{118}{112}
\]

Now, let's simplify \( \frac{118}{112} \):

\[
\frac{118}{112} = \frac{59}{56} \approx 1.05357
\]

In decimal form, this indicates that the width must be less than or equal to approximately \( 1.05 \) inches.

Next, we will calculate \( \frac{118}{112} \) in fraction form to see if it relates to the choices given. Since both terms in \( \frac{118}{112} \) can be simplified by dividing by 2, we get:

\[
\frac{59}{56} \text{ in.}
\]

Now, comparing with the available responses:

- **Responses**:
1. \( w \leq 34 \text{ in.} \)
2. \( w \leq \frac{3}{4} \text{ in.} \) (0.75)
3. \( w \leq 38 \text{ in.} \)
4. \( w \leq \frac{3}{8} \text{ in.} \) (0.375)
5. \( w \leq 258 \text{ in.} \)
6. \( w < 34 \text{ in.} \)

None of these options include \( w \leq \frac{59}{56} \).

However, given that \( \frac{59}{56} \) is approximately \( 1.05357 \), the closest valid width less than or equal to that value, among the choices, could logically be interpreted as **not being greater than 34 in.**

So, the most appropriate choice — given it satisfies the area constraint — is:

**w ≤ 34 in.**

Thus, the solution to the inequality that describes the possible width of the stamp is:

**w ≤ 34 in.**