The ratio of the number of tomato plants in Inessa's garden to the number of tomato plants in Ralph's garden was 5:6. After 1 2 the tomato plants from Inessa's garden were replanted into Ralph's garden, his garden had 850 tomato plants. How many tomato plants did Ralph's garden have in the first place?

Inessa = X

Ralph = Y

By the given ratio X/Y = 5/6

Solve for X: X = 5/6 * Y

Now Inessa gives 1/2 of hers to Ralph, which then totals 850"

Y + 1/2X = 850

Replace x:

Y + 1/2 * 5/6 * Y = 850

SImplify:

Y + 5/12Y = 850

Multiply both sides by 12 to remove the fraction:

12Y + 5Y = 10200

Simplify:

17Y = 10200

Divide both sides by 17:

y = 10200 / 17

y = 600

Ralph originally had 600 plants.