Dasha has 4 times more rose bushes in her garden than Anna. After 39 rose bushes were removed from Dasha's garden and then replanted into Anna's garden, the number of bushes in both gardens became the same. How many rose bushes did Dasha's garden have originally?
d = 4 a
d- 39 = a + 39
a = d/4
d - 39 = d/4 + 39
3 d/4 = 78
d/4 = 26
d = 4 * 26
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To solve this problem, let's break it down step by step.
Let's assume that Anna originally had "x" rose bushes in her garden.
According to the problem, Dasha had 4 times more rose bushes than Anna. Therefore, Dasha originally had 4*x rose bushes.
After some of Dasha's rose bushes were removed and replanted into Anna's garden, the number of rose bushes in both gardens became the same.
So, after 39 rose bushes were removed from Dasha's garden, she had 4*x - 39 rose bushes.
And after these 39 rose bushes were replanted in Anna's garden, she had x + 39 rose bushes.
Since the number of rose bushes in both gardens became the same, we can set up an equation:
4*x - 39 = x + 39.
To solve this equation, we need to isolate the variable x.
Let's simplify the equation:
4*x - x = 39 + 39
This simplifies to:
3*x = 78.
Now, we can solve for x by dividing both sides of the equation by 3:
x = 78 / 3
x = 26.
So, Anna originally had 26 rose bushes in her garden.
And since Dasha had 4 times more rose bushes than Anna, she originally had 4 * 26 = 104 rose bushes in her garden.