there are 55 blades of grass in 1 in.2 of the lawn. there are 230 blades of grass in 4 in.2 of the same lawn. how many blades of grass are in 3 in.2 of lawn

Online, "^" is used to indicate an exponent, e.g., in^2 = inches squared.

If there were 55 blades/square inch, then there would be 4 times that in 4 in^2 or 220. (your typo?)

In 3 in^2, there would be 3 * 55 = 165.

Not a typo. The book says 230 blades in 4 square inches.

This is what I came up with (may not be right):

X = # blades in 1 sq in

(X*4)+10 = 230 (blades in 4 sq in)

I surmised that (X*2)+5 = # blades in 2 inches

Therefore, (X*3)+7.5 = # Blades in 3 sq inches.

52.983

To solve this problem, you need to find the number of blades of grass in 3 in.² of the lawn using the given information.

First, calculate the number of blades of grass per square inch by dividing the total number of blades by the total square inches:

Number of blades per square inch = Total number of blades / Total square inches

For the first scenario, there are 55 blades of grass in 1 in.² of the lawn:

Number of blades per square inch (scenario 1) = 55

For the second scenario, there are 230 blades of grass in 4 in.² of the lawn:

Number of blades per square inch (scenario 2) = 230 / 4 = 57.5

Now, we have two values representing the number of blades per square inch in different scenarios. We can use this information to find the number of blades in 3 in.² of the lawn.

To find the number of blades in 3 in.², we can set up a proportion:

(Number of blades 1 in.²) / (Number of blades 3 in.²) = (Number of blades 1 in.²) / (Number of blades 4 in.²)

Using the values we have:

(55) / (Number of blades 3 in.²) = (55) / (57.5)

Cross-multiplying the equation:

55 * (Number of blades 3 in.²) = 55 * (57.5)

Now, you can solve for the number of blades of grass in 3 in.²:

(Number of blades 3 in.²) = (55 * 57.5) / (55) = 57.5

Therefore, there are 57.5 blades of grass in 3 in.² of the lawn. However, since you can't have a fraction of a blade, we round it down to the nearest whole number.

Hence, there are 57 blades of grass in 3 in.² of the lawn.