Question

the label on a \\(\frac{1}{3}\\)-pound bag of seeds states that it will cover an area of 137 square feet. what is the area that one pound of seeds will cover?\
on the double number line below, fill in the given values, then use multiplication to find the missing value. enter your answers as whole numbers, fractions, or mixed numbers.\
to enter a mixed number, press the \+\ key or click the \mixed number\ button.\
double number line image with square feet and pounds axes\
enter your final answer as a whole number, fraction, or mixed number in simplest form.

Explanation:

Step1: Identify the relationship

We know that $\frac{1}{3}$ pound of seeds covers 137 square feet. We need to find the area covered by 1 pound of seeds. Let \( x \) be the area covered by 1 pound of seeds. The relationship is proportional, so we can set up the equation: if $\frac{1}{3}$ pound corresponds to 137 square feet, then 1 pound corresponds to \( x \) square feet. Mathematically, this means \( \frac{1}{3} \times x = 137 \) (wait, no, actually, the rate is area per pound. So the rate \( r=\frac{\text{area}}{\text{pounds}} \). For $\frac{1}{3}$ pound, area is 137, so \( r = \frac{137}{\frac{1}{3}} \), but to find the area for 1 pound, we can think of it as: if $\frac{1}{3}$ pound gives 137, then 1 pound (which is 3 times $\frac{1}{3}$ pound) will give \( 137\times3 \).

Step2: Calculate the area for 1 pound

To find the area covered by 1 pound, we multiply the area covered by $\frac{1}{3}$ pound by 3 (since 1 pound is 3 times $\frac{1}{3}$ pound). So \( 137\times3 = 411 \).

Answer:

411