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# The ratio of trees to benches in a park is 4 to 1. If adding ten more

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Math Expert
Joined: 02 Sep 2009
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The ratio of trees to benches in a park is 4 to 1. If adding ten more  [#permalink]

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28 Sep 2016, 02:55
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91% (01:22) correct 9% (01:45) wrong based on 98 sessions

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The ratio of trees to benches in a park is 4 to 1. If adding ten more benches in the park changes the ratio to 4 to 3, how many trees are there in the park?

A. 5
B. 10
C. 15
D. 20
E. 25

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Posts: 6961
Re: The ratio of trees to benches in a park is 4 to 1. If adding ten more  [#permalink]

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28 Sep 2016, 04:34
1
Bunuel wrote:
The ratio of trees to benches in a park is 4 to 1. If adding ten more benches in the park changes the ratio to 4 to 3, how many trees are there in the park?

A. 5
B. 10
C. 15
D. 20
E. 25

Multiply initial ratio by a variable to convert these ratios to numbers..
So # of trees and # of benches are 4x and x..

New ratio= 4/3 = 4x/(x+10)......
4x+40=12x......8x=40.....x=5

Number of trees is 4x or 4*5=20

D
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Re: The ratio of trees to benches in a park is 4 to 1. If adding ten more  [#permalink]

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28 Sep 2016, 16:12
1
You can do this by plugging in the answer choices

if 10 trees then 2 Benches (4:1) now we add 10 benches new ratio is (10:12) - Not correct

Then we jump to D since number of trees must be higher

if 20 trees then 5 benches (4:1) and now we add 10 benches so new ratio is 20:15 (4:3) correct
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The ratio of trees to benches in a park is 4 to 1. If adding ten more  [#permalink]

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29 Sep 2016, 09:25
1
Bunuel wrote:
The ratio of trees to benches in a park is 4 to 1. If adding ten more benches in the park changes the ratio to 4 to 3, how many trees are there in the park?

A. 5
B. 10
C. 15
D. 20
E. 25

Originally $$\frac{T}{B} = \frac{4x}{x}$$

if we add 10benches=====> $$\frac{4x}{(x+10)}=\frac{4}{3}$$ ======> $$x=5$$

the number of trees is $$4x=4*5=20$$

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Re: The ratio of trees to benches in a park is 4 to 1. If adding ten more  [#permalink]

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02 Oct 2016, 01:20
1
The ratio of trees to benches in a park is 4 to 1
T : B = 4 : 1
so, T = 4B

Also,adding ten more benches in the park changes the ratio to 4 to 3 changes the ratio to -
T : B + 10 = 4 : 3
3T= 4(B+ 10)
3T= 4B + 40

replacing 4B= T from first equation

3T= T + 40
hence, T= 20

D
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Re: The ratio of trees to benches in a park is 4 to 1. If adding ten more  [#permalink]

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27 Feb 2017, 04:47
Let number of tree be 4x and benches be x
According to question 4x/(x+10) = 4/3. After solving, we get x = 5. Number of trees= 4x = 20. Option D
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Re: The ratio of trees to benches in a park is 4 to 1. If adding ten more  [#permalink]

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01 Mar 2017, 18:26
1
Bunuel wrote:
The ratio of trees to benches in a park is 4 to 1. If adding ten more benches in the park changes the ratio to 4 to 3, how many trees are there in the park?

A. 5
B. 10
C. 15
D. 20
E. 25

We are given that the ratio of trees to benches in a park is 4 to 1, or trees : benches = 4x : x

Since when 10 benches are added to the park the ratio becomes 4 to 3, we can create the following equation to determine x:

(4x)/(x + 10) = 4/3

12x = 4(x + 10)

3x = x + 10

2x = 10

x = 5

Thus, there are 4 x 5 = 20 trees in the park.

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Re: The ratio of trees to benches in a park is 4 to 1. If adding ten more  [#permalink]

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02 Mar 2017, 08:03
Bunuel wrote:
The ratio of trees to benches in a park is 4 to 1. If adding ten more benches in the park changes the ratio to 4 to 3, how many trees are there in the park?

A. 5
B. 10
C. 15
D. 20
E. 25

$$\frac{4x}{x + 10} = \frac{4}{3}$$

Or, $$12x + 4x = 40$$

Or, $$8x = 40$$

So, $$x = 5$$

So, No of trees will be 4*5 = 20

Thus, answer will be (D) 20
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Re: The ratio of trees to benches in a park is 4 to 1. If adding ten more &nbs [#permalink] 02 Mar 2017, 08:03
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