Question

A. What is the constant of proportionality between the number of square yards of ground to be covered and the number of scoops of grass seed needed? The field Archie will cover with grass seed has an area of 600 square yards. Grass Seed Area of Ground to Bo Covered 50 (square yards). Number of Scoops 2 100 150 200 4 6 8.

B. Write an equation that describes the relationship between the number of square yards (x) of ground to be covered and the number of scoops (y) of grass seed needed. Use the equation to determine the number of scoops of grass seed Archie needs to cover the entire field. Show or explain all your work.

Answer 1

The constant of proportionality is 0.06 scoops per square yard. The equation is y = 0.06x. Archie needs 36 scoops to cover the entire field.

Step-by-step explanation:

The constant of proportionality between the number of square yards of ground to be covered and the number of scoops of grass seed needed can be found by dividing the number of scoops by the area of ground to be covered. In this case, let's take the second set of data points: 100 square yards of ground and 6 scoops of grass seed. So, the constant of proportionality is 6 scoops ÷ 100 square yards = 0.06 scoops per square yard.

The equation that describes the relationship between the number of square yards (x) of ground to be covered and the number of scoops (y) of grass seed needed is y = 0.06x.

To determine the number of scoops of grass seed Archie needs to cover the entire field, we substitute the area of the field (600 square yards) into the equation: y = 0.06(600) = 36 scoops.