Q: The ratio of the number of plants that Keisha has to the number of plants Sam has is 1:5. After Sam gives Keisha 5 plants, the ratio of plants Keisha has to the plants Sam has will be 2:7. How many more plants will Sam have than Keisha after 5 plants are given?
(Target Audience: GMAT)
- 30
- 45
- 50
- 60
- 75
Answer: Option C
Explanation: Generic Way
Let K = # of plants that Keisha PRESENTLY has
Let S = # of plants that Sam PRESENTLY has
The ratio of the number of plants that Keisha has to the number of plants Sam has is 1:5
We can write: K/S = 1/5
Cross multiply to get: 5K = S
After Sam gives Keisha 5 plants, the ratio of plants Keisha has to the plants Sam has will be 2:7
After Sam gives Keisha 5 plants, we have
K + 5 = # of plants Keisha has
S – 5 = # of plants Sam has
So, we can write: (K +5)/(S – 5) = 2/7
Cross multiply to get: 7(K + 5) = 2(S – 5)
Expand: 7K + 35 = 2S – 10
Simplify: 7K – 2S = -45
We now have two equations with 2 variables:
5k = S
7K – 2S = -45
Take bottom equation and replace S with 5K to get: 7K – 2(5K) = -45
Simplify: -3K = -45
Solve: K = 15
So, Keisha PRESENTLY has 15 plants, which means Sam PRESENTLY has 75 plants
After Sam gives Keisha 5 plants, Keisha has 20 plants and Sam has 70 plants
How many more plants will Sam have than Keisha after 5 plants are given?
70 – 20 = 50
OPTION C
Explanation: HolaMaven Way
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 respectively
Ratio of 15 and 75 is 1:5, which is matching the condition in question.
Thus answer is Option C