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The ratio of the number of plants that Keisha has to the number
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27 Aug 2017, 02:03

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A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

70% (02:04) correct 30% (02:06) wrong based on 73 sessions

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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?

Re: The ratio of the number of plants that Keisha has to the number
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27 Aug 2017, 02:08

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 _________________

Abhishek Parikh Math Tutor Whatsapp- +919983944321 Mobile- +971568653827 Website: http://www.holamaven.com

Re: The ratio of the number of plants that Keisha has to the number
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27 Aug 2017, 02:32

HolaMaven wrote:

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?

A. 30 B. 45 C. 50 D. 60 E. 75

let the common ratio be x, so \(\frac{k}{s} = \frac{x}{5x}\) After s gives 5 to k, ratio becomes \(\frac{x+5}{5x-5}=\frac{2}{7}.....7x+35=10x-10.....3x=45...x=15\)

so the difference prior to exchange of 5 is (5-1)*x=4*15=60.. now when s gives 5 to k, difference reduces by 5+5=10...60-10=50 OR number = 15*1:15*4=15:75 after exchange of 5 it becomes = 15+5:75-5=20:70 so difference = 70-20=50

Re: The ratio of the number of plants that Keisha has to the number
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27 Aug 2017, 05:11

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Top Contributor

HolaMaven wrote:

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?

A. 30 B. 45 C. 50 D. 60 E. 75

Another approach...

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

The ratio of the number of plants that Keisha has to the number
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27 Aug 2017, 11:22

HolaMaven wrote:

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?

A. 30 B. 45 C. 50 D. 60 E. 75

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