1. There are 4 pounds of lawn seed to a bag. Three pounds of lawn seed covers 1800 square feet. How many bags are needed to cover 8400 square feet? Write and solve a proportion.
So the only part of the proportion I currently have written is: 1800/ = 8400/x
I'm not sure how to write 3 pounds out of 4 pounds to a bag. Which should be the denominator in 1800/.
2. Consider the proportions m/n = 1/2 and n/k = 2/5.
What is the ratio m/k?
4/1800 = x/8400
m/k = m/n * n/k = 1/5
you and me
15
1. To find out how many bags are needed to cover 8400 square feet, you can set up a proportion using the given information. Let's solve it step by step.
First, let's determine the ratio of pounds to square feet. We know that 3 pounds of lawn seed covers 1800 square feet. So, the ratio is 3 pounds / 1800 square feet.
Next, we need to find the ratio for 4 pounds, as there are 4 pounds of lawn seed in a bag. Since the ratio of pounds to square feet is constant, we can write the proportion as follows:
3 pounds / 1800 square feet = 4 pounds / x square feet
Now, we can use cross-multiplication to solve for x:
3x = 4 * 1800
3x = 7200
x = 7200 / 3
x = 2400
Therefore, you would need one bag to cover 2400 square feet.
Now, to find out how many bags are needed to cover 8400 square feet, we write the final proportion:
3 pounds / 1800 square feet = 4 pounds / 2400 square feet
We need to determine the value of x in the proportion:
3 / 1800 = 4 / 2400
To solve this proportion, you can cross-multiply:
3 * 2400 = 4 * 1800
7200 = 7200
So, the proportion is satisfied, and the value of x is 2400. Therefore, you would need 4 bags to cover 8400 square feet.
2. To find the ratio m/k, we need to manipulate the given proportions and combine them.
Given:
m/n = 1/2
n/k = 2/5
To find m/k, we can multiply these proportions:
(m/n) * (n/k) = (1/2) * (2/5)
By canceling out the common factor of 2, we get:
(m/n) * (1/5) = 1/5
Now, simplify the equation:
m/5n = 1/5
Multiply both sides by 5:
5 * (m/5n) = 5 * (1/5)
This cancels out on the left side, leaving:
m/n = 1
Therefore, the ratio m/k is 1.