Questions: Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. Fabric was bought at X-mart, because their price of 5 per square foot was better than Y-mart's price of 14 per square yard.

Solution Steps

To determine whether the statement makes sense, we need to compare the price per square foot at X-mart with the price per square foot at Y-mart. Since Y-mart's price is given per square yard, we need to convert it to a price per square foot. There are 9 square feet in a square yard, so we divide Y-mart's price by 9 to find the price per square foot. Then, we compare the two prices to see which is cheaper.

The price at Y-mart is given as \( \$14 \) per square yard. To convert this to a price per square foot, we use the conversion factor that \( 1 \) square yard equals \( 9 \) square feet. Thus, the price per square foot at Y-mart is calculated as follows:

\[ \text{Price per square foot at Y-mart} = \frac{14}{9} \approx 1.5556 \]

Now we compare the price per square foot at X-mart and Y-mart. The price at X-mart is \( \$5 \) per square foot, while the price at Y-mart is approximately \( 1.5556 \) per square foot. We check if X-mart's price is cheaper:

\[ 5 < 1.5556 \]

This statement is false, indicating that X-mart is not cheaper than Y-mart.

Final Answer