Ratio query

[Mollumophead]

Hi all,
trying my best to get my head around this but have hit a senior moment so I hope you will help me out.

There are between 10 and 30 animals on a farm
the ratio of cows to sheep is 2:3
Investigate finding the possible number of cows and sheep on the farm
how would you approach this ? Is it as simple up multiplying each one by a Number until you hit 10 and then continue until you hit 30 ?
( old and decrepit attempting to improve my maths exam result after 45 years ) be kind,

 

[Steven G]

Why can it be 2:3, that is you have 2 cows and 3 sheep? Sure you say that there must be between 10 and 30 animals on the farm but there can be other animals!

If there are no other animals then you are correct. 2:3 = 4:6 = 6:9 = 8:12 = 10:15 = 12:18 = 14:21 =.... Just use the ratios that add up to between 10 and 30.

 

[Mollumophead]

Thank you!
seemed too easy!
overthinking is my enemy .

 

[HallsofIvy]

Since the ratio of cows to sheep is 2:3 and 2+ 3= 5 the total number or cows and sheep must be a multiple of 5. Assuming that cows and sheep are the only animals on the farm, since there are "between 10 and 30 animals on the farm" there could be total of 3(5)= 15 animals (so 3(2)= 6 cows and 3(3)= 9 sheep), 4(5)= 20 animals (so 4(2)= 8 cows and 4(3)= 12 sheep), or 5(5)= 25 animals (so 5(2)= 10 cows and 5(30)= 15 sheep).

(If the "between 10 and 30 animals" was inclusive add 2(5)= 10 animals (2(2)= 4 cows and 2(3)= 6 sheep) and 6(5)= 30 animals (6(2)= 12 cows and 6(3)= 18 sheep).)

 

[Mollumophead]

Thank you. Feeling rather dim now, Im trying to keep my mind working after serious illness, I used to be good at maths !
when you explain it seems perfectly straightforward,
thank you