Answer:
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.
