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?

17

Step-by-step explanation:

Let x represent the number of roses in the first yard and y represent the number of roses in the second yard.

The first yard has 10 fewer roses than the second yard; this gives us

x = y-10

If we transplant 9 roses from the second yard to the first, this adds 9 roses to the first yard, giving us x+9.

This also makes the first yard, now x+9, equal to twice as much as the second yard (after the 9 come out); this gives us 2(y-9) and the equation

x+9 = 2(y-9)

From the first equation, we know that x = y-10; this gives us

y-10+9 = 2(y-9)

Combining like terms on the left, we have

y-1 = 2(y-9)

Using the distributive property on the right,

y-1 = 2(y)-2(9)

y-1 = 2y-18

Add 1 to each side:

y-1+1 = 2y-18+1

y = 2y-17

Subtract 2y from each side:

y-2y = 2y-17-2y

-1y = -17

Divide both sides by -1:

-1y/-1 = -17/-1

y = 17

There are 17 roses in the second yard, and 17-10 = 10 roses in the first one.

Number of roses in second yard=17

Step-by-step explanation:

We have to find number of roses in the second yard.

Let roses in second yard=x

In the first yard there are 10 roses less than in the second one.

Then, roses in first yard=x-10

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.

now, x-10+9=2(x-9)

i.e. x-1=2x-18

   x=17

Hence, number of roses in second yard=17

multiplication is multiplication.   it might feel harder depending on what level of math you are in, but generally it will be the same old stuff, while implementing some new concepts and methods of solving work.