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?

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25-09-2019
Mathematics

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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?

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luisejr77 luisejr77 · Answer 1 · 2019-09-27T02:32:57+02:00

Answer: 104 roses.

Step-by-step explanation:

Let be "d" the number of bushes rose Dasha's garden has originally and "a" the number of bushes rose Anna's garden originally.

Originally, Dasha has 4 times more rose bushes in her garden than Anna. This is:

[tex]d=4a[/tex] [Equation 1]

The number of bushes in both gardens became the same after removing 39 rose bushes from Dasha's garden and replanted them into Anna's garden. This is:

[tex]d-39=a+39[/tex] [Equation 2]

Knowing this, we can substitute the [Equation 1] into [Equation 2] and solve for "a":

[tex](4a)-39=a+39\\\\4a-a=39+39\\\\3a=78\\\\a=\frac{78}{3}\\\\a=26[/tex]

Substituting this value into [Equation 1], we get:

[tex]d=4(26)\\\\d=104[/tex]