This is a 2-part problem and I solved the first part, but can't get the second.
Brad has a circular garden with a radius of 3 feet. There are 54 flowers in his garden. He wants to plant different flowers in a 1-foot border all around his garden. What is the area, in square feet, of the border for Brad's garden? Use 3.14 for pie. My answer is 50.24 square feet.
Here's the part I can't get -
Brad wants the ratio of the number of flowers in his border to the area of his border to be the same as the ratio of the number of flowers in his original garden to the area of his original garden. How many flowers does Brad need for his border?
area of garden = 9(3.14) = appr 28.26
area of garden + border = 16(3.14) = 50.25
area of border = 50.25-28.26 = 21.98 ft^2
so that disagrees with your answer
ration of flowers : border = ratio of flowers : original garden
x/21.98 = 54/28.26
x = 54(21.98)/28.26 = 42
Thank you! I actually just found my mistake and my answer matches yours :)
To solve the second part of the problem, we need to start by finding the area of Brad's original garden and the number of flowers in his original garden.
The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius. So for Brad's original garden, with a radius of 3 feet, the area is:
A = 3.14 * 3^2 = 3.14 * 9 = 28.26 square feet
Now we can set up a ratio to solve for the number of flowers in the border. The ratio of the number of flowers to the area in the original garden should be equal to the ratio of the number of flowers to the area in the border.
Let's call the number of flowers in the border "x". The area of the border is equal to the area of the larger circle minus the area of the smaller circle. The larger circle has a radius of 4 feet (3 feet + 1 foot border), and the smaller circle has a radius of 3 feet. So the area of the border is:
A_border = π(4^2) - π(3^2) = 16π - 9π = 7π square feet
Now we can set up the ratio equation:
Number of flowers in original garden / Area of original garden = Number of flowers in border / Area of border
54 / 28.26 = x / (7π)
To solve for x, we multiply both sides of the equation by (7π):
54 * (7π) / 28.26 = x
Now we can calculate the value of x:
x = 378π / 28.26 ≈ 43.34
So Brad would need approximately 43.34 flowers for his border.