A research garden is divided into sections, each with an area of \(\frac{3}{4}\) square yard. An area of \(\frac{2}{3}\) square foot within each section is planted with beans. What unit rate gives the number of square feet planted with beans per square yard of garden?
Answer (2)
To find the unit rate of the number of square feet planted with beans per square yard of garden, we need to convert square yards to square feet because the area planted with beans is given in square feet. We know that 1 square yard is equivalent to 9 square feet. Therefore, to find the area of beans planted, we multiply the area planted with beans per section (2/3 square foot) by the total number of sections, which is given by the total area in square yards divided by the area per section (3/4 square yard).
First, we convert the area of each section into square feet:
3/4 square yards × 9 square feet/square yard = 27/4 square feet.
Then, we consider the beans' planting area:
2/3 square foot / (27/4 square feet) = (2/3) × (4/27) = 8/81.
Therefore, the unit rate is 8/81 square feet of beans planted per square yard of garden.
To find the unit rate of beans planted per square yard, we converted the section area from square yards to square feet and compared the area planted with beans to the section area. The unit rate is 81 8 square feet of beans planted per square yard of garden.
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