Question

40) There are 55 blades of grass in 1 in2 of lawn. There are 230 blades of grass in 4 in2 of the same lawn. How many blades of grass are in 3 in2 of lawn?

Answer 1

Answer:

172 blades

Step-by-step explanation:

Let x be the area of the lawn.

Let y be the number of blades of grass.

To find the equation, we will use point slope form

y-y1 = m(x-x1)

m = slope of the line

(x1,y1) = point on the line

m = (y2 - y1) / (x2 - x1)

x1 = 1, y1 = 55

x2 = 4, y2 = 230

m = (230 - 55) / (4 - 1)

m = 175/3

Put m = 175/3 into y - y1 = m(x - x1)

y - 55 = 175/3(x - 1)

y - 55 = 175/3(x) - 175/3

y = 175/3(x) - 175/3 + 55

y = 175/3(x) - 175/3 + 165/3

y = 175/3(x) - 10/3

To find how many blades of grass are there in 3in^2 of lawn, put X = 3 in the equation y = 175/3(x) - 10/3

y = 175/3(3) - 10/3

y = 175 - 10/3

y = (525 - 10)/3

y = 515 / 3

y = 171.6667

y = 172 (approximately)

There are 172 blades of grass