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The ratio between the number of sheep and the number of horses at the

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The ratio between the number of sheep and the number of horses at the  [#permalink]

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New post 14 Jun 2016, 07:09
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The ratio between the number of sheep and the number of horses at the Stewart farm is 4 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm?

A. 18
B. 28
C. 32
D. 56
E. 60

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Re: The ratio between the number of sheep and the number of horses at the  [#permalink]

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New post 14 Jun 2016, 07:24
Let the number of sheeps and horses be 4x and 7x.

Now total number of horses = total consumption of horse food/consumption per horse = 12880/230 = 56, which is equal to 7x. => x = 8

Sheeps = 4x = 4*8 = 32. Hence C.
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Re: The ratio between the number of sheep and the number of horses at the  [#permalink]

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New post 14 Jun 2016, 16:45
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Bunuel wrote:
The ratio between the number of sheep and the number of horses at the Stewart farm is 4 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm?

A. 18
B. 28
C. 32
D. 56
E. 60


Each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day.
12,800/230 = 56
So, there are 56 horses

We can use EQUIVALENT RATIOS to determine the number of sheep
sheep/horses: 4/7 = x/56
Cross multiply to get: (4)(56) = 7x
Divide both sides by 7 to get: (4)(56)/(7) = x
Solve: x = 32

Answer:

The following video contains the skills needed to answer this question

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The ratio between the number of sheep and the number of horses at the  [#permalink]

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New post 14 Jun 2016, 22:22
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Bunuel wrote:
The ratio between the number of sheep and the number of horses at the Stewart farm is 4 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm?

A. 18
B. 28
C. 32
D. 56
E. 60


Actual number of horses = 12,880/230 (hold it since it is a harder calculation)

Ratio multiplier = 1288/(23*7)

Actual number of sheep = 1288/(23*7) * 4.
First divide 1288 by 7 to get: 184*4/23
Use the last digit to figure out that 23 will go 8 times into 184. Confirm. 8*4 = 32

Answer (C)
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Re: The ratio between the number of sheep and the number of horses at the  [#permalink]

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New post 26 Jun 2017, 07:49
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Let s= sheep and h= horses
s:h --> 4x:7x=11x set 7x equal to the total amount of horse food. 7x=12,880 --> x=1840--> divide that by 230 ounces to get the number of horses -->x=8. Now you have the multiplier and can find the number of sheep: 4*8= 32 !
Answer (C)
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Re: The ratio between the number of sheep and the number of horses at the  [#permalink]

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New post 28 Jun 2017, 16:56
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Bunuel wrote:
The ratio between the number of sheep and the number of horses at the Stewart farm is 4 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm?

A. 18
B. 28
C. 32
D. 56
E. 60


Since each horse is fed 230 ounces per day and the farm needs a total of 12,880 ounces of horse food per day, there are 12880/230 = 56 horses on the farm.

Since the ratio of sheep to horses is 4 : 7, or 4x : 7x, we know that 7x = 56, and thus x = 8. Thus, there are 4 x 8 = 32 sheep on the farm.

Answer: C
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Re: The ratio between the number of sheep and the number of horses at the  [#permalink]

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New post 29 Jun 2017, 15:30
The ratio between the number of sheep and the number of horses at the Stewart farm is 4 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm?

\(\frac{Sheep}{Horses} = \frac{4}{7}\)


\(Food Per Horse = 230 Ounces\)


\(Total Horse Food = 12,880\)


\(Total Horses = \frac{Total Horse Food}{Food Per Horse}\)


\(Total Horses = \frac{12,880}{230}\)


Lets substitute this value in the original ratio:


\(\frac{Sheep}{Horses} = \frac{4}{7}\)


\(Total Sheep = \frac{4}{7} * \frac{12,880}{23}\)


\(Total Sheep = 4 * 8\)


\(Total Sheep = 32\)


Hence, Answer is C
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Re: The ratio between the number of sheep and the number of horses at the   [#permalink] 29 Jun 2017, 15:30
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