One garden had 5 times as many raspberry bushes as a second garden. After 22 bushes are transplanted from the first garden to the second garden, the number of raspberry bushes in the gardens are the same. How many bushes did each garden have originally?
The first garden had (blank) raspberry bushes the second garden had (blank) raspberry bushes
The bot isn’t correct
I apologize for the mistake. Let's approach the problem again.
Let's assume that the second garden initially had "x" raspberry bushes.
According to the problem, the first garden had 5 times as many raspberry bushes as the second garden. So, the first garden initially had 5x raspberry bushes.
After 22 bushes are transplanted from the first garden to the second garden, the number of raspberry bushes becomes the same in both gardens. This means that the first garden now has 5x - 22 bushes, and the second garden still has x bushes.
Since the number of raspberry bushes is the same in both gardens, we can write the equation:
5x - 22 = x
By solving this equation, we can find the value of x, which is the number of raspberry bushes in the second garden.
4x = 22
x = 5.5
Since we can't have a fractional number of bushes, this means that our initial assumption was incorrect. The second garden cannot have had 5.5 raspberry bushes.
Let's try a different approach:
Let's assume that the second garden initially had "y" raspberry bushes.
According to the problem, the first garden had 5 times as many raspberry bushes as the second garden. So, the first garden initially had 5y raspberry bushes.
After 22 bushes are transplanted from the first garden to the second garden, the number of raspberry bushes becomes the same in both gardens. This means that the first garden now has 5y - 22 bushes, and the second garden has y + 22 bushes.
Since the number of raspberry bushes is the same in both gardens, we can write the equation:
5y - 22 = y + 22
Simplifying the equation:
4y = 44
y = 11
So the second garden originally had 11 raspberry bushes.
Using this value, we can find the number of raspberry bushes in the first garden:
5y - 22 = 5(11) - 22 = 55 - 22 = 33
So the first garden originally had 33 raspberry bushes.
What about the second one
Apologies for missing the second part of the question. Let's address it:
The first garden originally had 33 raspberry bushes and the second garden originally had 11 raspberry bushes.
The first one isn’t correct
Apologies for the mistake. Let's reevaluate the problem:
Let's assume that the second garden initially had "y" raspberry bushes.
According to the problem, the first garden had 5 times as many raspberry bushes as the second garden. So, the first garden initially had 5y raspberry bushes.
After 22 bushes are transplanted from the first garden to the second garden, the number of raspberry bushes becomes the same in both gardens. This means that the first garden now has 5y - 22 bushes, and the second garden has y + 22 bushes.
Since the number of raspberry bushes is the same in both gardens, we can write the equation:
5y - 22 = y + 22
Simplifying the equation:
4y = 44
y = 11
So the second garden originally had 11 raspberry bushes.
Using this value, we can find the number of raspberry bushes in the first garden:
5y - 22 = 5(11) - 22 = 55 - 22 = 33
So the first garden originally had 33 raspberry bushes.
Let's call the number of raspberry bushes in the second garden "x".
According to the first sentence, the first garden had 5 times as many raspberry bushes as the second garden. So the number of bushes in the first garden is 5x.
After 22 bushes are transplanted from the first garden to the second garden, the number of raspberry bushes in the gardens is the same. This means that the second garden now has x + 22 bushes, and the first garden has 5x - 22 bushes.
Since the number of raspberry bushes is the same in both gardens, we can write the equation:
x + 22 = 5x - 22
By solving this equation, we can find the value of x, which is the number of raspberry bushes in the second garden.
x + 22 = 5x - 22
4x = 44
x = 11
So the second garden originally had 11 raspberry bushes.
Using this value, we can find the number of raspberry bushes in the first garden:
5x - 22 = 5(11) - 22 = 33
So the first garden originally had 33 raspberry bushes.