SOLUTION: 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 of the tomato plants from Inessa’s garden were repla

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 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 of the tomato plants from Inessa’s garden were repla      Log On


   

Question 1124516: 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 of the tomato plants from Inessa’s garden were replanted into Ralph’s garden, Ralph’s garden had 850 tomato plants. How many tomato plants did Ralph’s garden have in the first place?
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the number in Inessa’s garden
Let +b+ = the number in Ralph’s garden
————————
(1) +a%2Fb+=+5%2F6+
(1) +a+=+%285%2F6%29%2Ab+
————————————-
(2) +b+%2B+%281%2F2%29%2Aa+=+850+
Plug (1) into (2)
(2) +b+%2B+%281%2F2%29%2A%285%2F6%29%2Ab+=+850+
Multiply both sides by +12+
(2) +12b+%2B+5b+=+10200+
(2) +17b+=+10200+
(2) +b+=+600+
Ralph’s garden had 600 originally
——————————
Check:
(1) +a+=+%285%2F6%29%2A600+
(1) +a+=+500+
+a+%2B+b+=+500+%2B+600+
inessa gives +500%2F2+=+250+ to Ralph
Now Ralph has +250+%2B+600+=+850+
OK

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


With the given ratio of 5:6, let 5x be the number in Inessa's garden and 6x be the number in Ralph's garden.

In the replanting, half of the plants in Inessa's garden are mover to Ralph's garden.

Now we could say the number of plants moved from Inessa's garden to Ralph's garden is 2.5x, or (5/2)x. But if we want to avoid working with fractions or decimals, we can redefine the original numbers in the two gardens as 10x and 12x.

So Ralph started with 12x plants, and 5x plants (half of Inessa's 10x) were moved to his garden.

That gives him 17x plants; and the number in his garden is 850. So 17x = 850; x = 50.

Then the number originally in Ralph's garden is 12x = 600.