Question

A postage stamp is being designed with a height of one one over 2 in the area must be no greater than 1 1/8 in what is the solution to an inequality that describes the possible with off the stamp A w < 3/4 inches B w < 2 5/8 C w < 3/4 inches D w < 3/8 inches

Answer 1

To solve the problem, we need to use the formula for the area of a rectangle, which is given by the formula:

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

In this case, the height of the postage stamp is given as \(1\frac{1}{2}\) inches, which can be converted to an improper fraction:

\[
1\frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \text{ inches}
\]

The maximum area of the stamp is given as \(1\frac{1}{8}\) inches, which can also be converted to an improper fraction:

\[
1\frac{1}{8} = 1 + \frac{1}{8} = \frac{8}{8} + \frac{1}{8} = \frac{9}{8} \text{ square inches}
\]

Next, we set up the inequality using the area formula. Let \(w\) represent the width of the stamp. The inequality representing the area constraint is:

\[
\frac{3}{2} \times w \leq \frac{9}{8}
\]

To isolate \(w\), divide both sides of the inequality by \(\frac{3}{2}\):

\[
w \leq \frac{9}{8} \div \frac{3}{2}
\]

When dividing by a fraction, it is equivalent to multiplying by its reciprocal:

\[
w \leq \frac{9}{8} \times \frac{2}{3} = \frac{9 \times 2}{8 \times 3} = \frac{18}{24} = \frac{3}{4}
\]

So the solution to the inequality that describes the possible widths of the stamp is:

\[
w \leq \frac{3}{4}
\]

Thus, the correct answer to the multiple choice question is:

**A. \(w < \frac{3}{4}\) inches** (assuming "A" includes "<" instead of "≤").