Question

In the first yard there are 10 roses less than in the second one. If 9 roses were transplanted from the second yard to the first one, then the first yard would have 2 times more roses than the second one. How many roses are there in the second yard?

Answer 1

Answer:

17

Step-by-step explanation:

Let x be the number of roses in the first yard. If in the first yard there are 10 roses less than in the second one, then in the second yard there are x+10 roses.

If 9 roses were transplanted from the second yard to the first one, then in the first yard the number of roses is x+9 and the number of roses in the second yard becomes x+10-9=x+1. After transplantation the first yard would have 2 times more roses than the second one, thus

$\dfrac{x+9}{x+1}=2\Rightarrow x+9=2(x+1),\\ \\x+9=2x+2,\\ \\2x-x=9-2,\\ \\x=7.$

There are x+10=7+10=17 roses in the second yard.