The ratio of North American Butterflies to South American butterflies at a butterfly park is 8:3.
The ratio of South American butterflies to European butterflies is 3:2.
There are 32 North American butterflies at the butterfly park.
How many South American butterflies are there?
And how many European butterflies are there?
NAB : SAB = 8 : 3
SAB : EB = 3 : 2
notice the term for SAB is 3 in both ratios, so we can say
NAB : SAB : EB = 8 : 3 : 2 OR 8x : 3x : 2x
"There are 32 North American butterflies" ----> 8x = 32
solve for x, then you can find any of the 3 cases.
To find out how many South American butterflies there are, we can use the ratio between North American and South American butterflies. We know that the ratio of North American butterflies to South American butterflies is 8:3.
Given that there are 32 North American butterflies, we can set up the following proportion:
North American butterflies / South American butterflies = 8/3
We can solve this proportion by cross-multiplying and then dividing:
32 / South American butterflies = 8 / 3
Cross-multiplying, we get:
(32)(3) = (8)(South American butterflies)
96 = 8(South American butterflies)
Dividing both sides by 8, we find:
South American butterflies = 12
Therefore, there are 12 South American butterflies at the butterfly park.
To find out how many European butterflies there are, we can use the ratio between South American and European butterflies. We know that the ratio of South American butterflies to European butterflies is 3:2.
Knowing that there are 12 South American butterflies, we can set up the following proportion:
South American butterflies / European butterflies = 3/2
Again, we can solve this proportion by cross-multiplying and then dividing:
12 / European butterflies = 3 / 2
Cross-multiplying, we get:
(12)(2) = (3)(European butterflies)
24 = 3(European butterflies)
Dividing both sides by 3, we find:
European butterflies = 8
Therefore, there are 8 European butterflies at the butterfly park.