The ratio of the number of plants that Keisha has to the number

The easiest number to work with is 50
Question is asking number of extra plants Sam has after the giving and taking process is done.
Using Option C
if 50 extra plants, then number of plants each of them has is 20 and 70 (2:7 ratio)
Now since Sam has given 5 plants to Keisha, plants available to both of them before exchange is 70+5 = 75 and 20-5 = 15
Ratio of 15 and 75 is 1:5, which is matching our condition in question.
Thus answer is Option C

Use x as a multiplier with the original ratio. Add and subtract 5 from that ratio, and set LHS equal to new ratio. Solve for x to yield how many plants each person had originally. Then calculate totals after the exchange.

Ratio of K's plants to S's plants:\(\frac{K}{S}\) = \(\frac{(1)x}{5x}\)

S gives K five plants. Account for it twice. The total quantities of both people have changed: \(\frac{x + 5}{5x -\\
5}\)

. . . and after S gives K the plants, the new ratio is 2:9

\(\frac{x + 5}{5x -\\
5}\) = \(\frac{2}{9}\)

10x - 10 = 7x + 35
3x = 45
x = 15 --> the multiplier for the original ratio quantities

So K had x = 15 plants
And S had 5x = 75 plants

K now has 5 more = 20
S now has 5 fewer = 70

How many more plants does S have after five are given? 70 - 20 = 50

Answer C

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