The ratio of cows to horses at a farm is 4:7. The number of horses at the farm is 28. What is the number of cows?

Question

The ratio of cows to horses at a farm is 4:7. The number of horses at the farm is 28. What is the number of cows?

Answer 1

This problem is asking you to expand the ratio 4:7 to a larger population. Think of it like this: 

here are the Cows: CCCC and here are the horses: HHHHHHH. Now, what if there are twice as many, but the relationship is the same? then we'd have: 

 

CCCC         HHHHHHH

CCCC         HHHHHHH

or

8 cows to 14 horses. 

 

so, what is the multiplier that would give us 28 horses? It is 4! (Since we started with 7 horses) 

Can you multiply the number of cows we started with by the same number? YES! 

 

we end up with: 

16 cows and 28 horses. 

 

This is the same process as expanding a fraction: 4/7 = 16/28... both are the same fraction. 

Answer 2

Set up a proportion:

 

  4 cows              x cows

---------------  =  ---------------

 7 horses           28 horses

 

Cross multiply:

 

4*28 = 7x

 

Solve for x, the number of cows.