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

17

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.

Answer 2

Number of roses in second yard=17

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