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The ratio of toddlers to infants at a day care center is 7 to 3. If

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The ratio of toddlers to infants at a day care center is 7 to 3. If  [#permalink]

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New post 19 Oct 2016, 23:33
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The ratio of toddlers to infants at a day care center is 7 to 3. If twelve more infants join the day care to change the ratio to 7 to 5, how many toddlers are there at this day care center?

A. 24
B. 36
C. 42
D. 72
E. 120

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Re: The ratio of toddlers to infants at a day care center is 7 to 3. If  [#permalink]

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New post 20 Oct 2016, 02:38
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answer: C

initial ratio is 7:3
let them be 7x and 3x

12 added to 3x; new ratio will be 7x/(3x+12) = 7:5

solving the equation we get 7x = 42 8-)
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Re: The ratio of toddlers to infants at a day care center is 7 to 3. If  [#permalink]

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New post 20 Oct 2016, 08:06
Bunuel wrote:
The ratio of toddlers to infants at a day care center is 7 to 3. If twelve more infants join the day care to change the ratio to 7 to 5, how many toddlers are there at this day care center?

A. 24
B. 36
C. 42
D. 72
E. 120


5x - 3x = 12

So, 2x = 6

hence no of toddlers is 6*7 =42

Answer will be (C) 42

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Re: The ratio of toddlers to infants at a day care center is 7 to 3. If  [#permalink]

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New post 20 Oct 2016, 08:52
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Top Contributor
Bunuel wrote:
The ratio of toddlers to infants at a day care center is 7 to 3. If twelve more infants join the day care to change the ratio to 7 to 5, how many toddlers are there at this day care center?

A. 24
B. 36
C. 42
D. 72
E. 120


Here's a different solution.
If the original toddlers to infant ratio is 7 to 3, then there are many different possible scenarios. Here are a few possibilities:
- 7 toddlers and 3 infants
- 14 toddlers and 6 infants
- 21 toddlers and 9 infants
- 28 toddlers and 12 infants
.
.
.
IMPORTANT: Notice that the number of toddlers is always divisible by 7
So, the correct answer must be divisible by 7

When we check the answer choices, we see that we can ELIMINATE A, B, D and E

Answer:

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Re: The ratio of toddlers to infants at a day care center is 7 to 3. If  [#permalink]

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New post 20 Oct 2016, 17:38
The ratio of toddlers to infants at a day care center is 7 to 3. If twelve more infants join the day care to change the ratio to 7 to 5, how many toddlers are there at this day care center?

A. 24
B. 36
C. 42
D. 72
E. 120

t/i = 7/3

t/i+12 =7/5

5t =7i + 84

3t = 7i

subsitute , t =84/2 =42
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Re: The ratio of toddlers to infants at a day care center is 7 to 3. If  [#permalink]

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New post 20 Oct 2016, 22:42
Current ratio of Toddler to Infant = 7:3

After addition of 12 infants:

\(\frac{7x}{(3x+12)}\) = \(\frac{7}{5}\)

X = 6

So No of Toddlers = 7*6 = 42.

Option C
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Re: The ratio of toddlers to infants at a day care center is 7 to 3. If  [#permalink]

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New post 21 Oct 2016, 10:05
Let, Toddler be x and Infant be y

From given Information,
x/y=7/3

Hence, x=7y/3----(1)

Now, 12 more infants are added which change the ratio to 7/5

x/(y+12)=7/5----(2)

Using value of x from equation (1)

7y/3(y+12)=7/5

Solving we get,

y=18

Substituting value in the equation (1)
We Get,

x=42.

Ans:- Hence Number of Toddlers is 42.

----------------------------------------------
Alternative Solution(Shortcut :P):

If we observer, the value of infant is changing and value of toddler is constant in the ratio which is 7.

Only option which is multiple of 7 is 42.

Once we get this we can cross verify it using equations (1) and (2).
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The ratio of toddlers to infants at a day care center is 7 to 3. If  [#permalink]

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New post 27 Oct 2016, 20:07
7x/(3x+12) = 7/5

35x=7(3x+12)
35x=21x+84
14x=84
x=6

7x= # of toddlers --> 7(6) = 42
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Re: The ratio of toddlers to infants at a day care center is 7 to 3. If  [#permalink]

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