The ratio of North American butterflies to South American butterflies at a butterfly park is 5:3. The ratio of South American butterflies to European butterflies is 3:2. There are 30 North American butterflies at the butterfly park.
a. How many South American butterflies are there?
b. How many European butterflies are there?
I have not done this type of a math problem before and really don't know where to begin on it or how to figure this out with ratios. Please help
I misread the question.
Should have been North American = 30 , not European.
I also noticed that I answered the same question back in 2014 without making that error,
look at the first of the Related Questions below.
since SA to E is 3:2
let SA be 3x and E be 2x
given E = 30
so 2x = 30
x = 15
So we know there are 3x or 45 South American and 30 Europeans, (note 45:30 = 3:2)
also NA : SA = 5:3
let NA be 5y and SA be 3y
but we know 3y = 45
y = 15
so the number of North American butterflies
= 5y or 75.
(again, note that 75: 45 = 5 :3)
No problem! Let's break this down step-by-step.
Step 1: Find the ratio of North American butterflies to South American butterflies.
The ratio of North American butterflies to South American butterflies is given as 5:3. This means that for every 5 North American butterflies, there are 3 South American butterflies.
Step 2: Use the ratio to find the number of South American butterflies.
Since we know that there are 30 North American butterflies, we can use the ratio to find the number of South American butterflies.
To do this, we can set up a proportion:
5 North American butterflies / 3 South American butterflies = 30 North American butterflies / x South American butterflies
Cross-multiplying, we get:
5x = 3 * 30
Simplifying the equation:
5x = 90
Dividing both sides by 5, we find:
x = 18
So, there are 18 South American butterflies at the butterfly park.
Step 3: Find the ratio of South American butterflies to European butterflies.
The ratio of South American butterflies to European butterflies is given as 3:2. This means that for every 3 South American butterflies, there are 2 European butterflies.
Step 4: Use the ratio to find the number of European butterflies.
Since we know that there are 18 South American butterflies, we can use the ratio to find the number of European butterflies.
To do this, we can set up a proportion:
3 South American butterflies / 2 European butterflies = 18 South American butterflies / y European butterflies
Cross-multiplying, we get:
3y = 2 * 18
Simplifying the equation:
3y = 36
Dividing both sides by 3, we find:
y = 12
So, there are 12 European butterflies at the butterfly park.
To summarize:
a. There are 18 South American butterflies at the butterfly park.
b. There are 12 European butterflies at the butterfly park.
To solve this problem, we need to use the concept of ratios and create a system of equations to find the unknown quantities. Here's how you can approach it:
Let's start by assigning variables to the unknown quantities:
- Let's call the number of South American butterflies "S".
- Let's call the number of European butterflies "E".
Given information:
1. The ratio of North American butterflies to South American butterflies is 5:3. This means that for every 5 North American butterflies, there are 3 South American butterflies. Since we know there are 30 North American butterflies, we can set up the following equation:
(Number of North American butterflies) / (Number of South American butterflies) = 5/3
30 / S = 5/3
2. The ratio of South American butterflies to European butterflies is 3:2. This means that for every 3 South American butterflies, there are 2 European butterflies. We can set up the following equation:
(Number of South American butterflies) / (Number of European butterflies) = 3/2
S / E = 3/2
Now we have a system of two equations:
Equation 1: 30 / S = 5/3
Equation 2: S / E = 3/2
To solve this system, we can use the method of substitution. Rearrange Equation 1 to isolate S:
30 / S = 5/3
Multiply both sides of the equation by S (to remove the denominator):
30 = 5S / 3
Multiply both sides by 3 to get rid of the fraction:
90 = 5S
Divide both sides by 5:
S = 18
Now that we have found the value of S, we can substitute it into Equation 2 to find the value of E:
18 / E = 3/2
Cross-multiply to solve for E:
2 * 18 = 3 * E
36 = 3E
Divide both sides by 3:
E = 12
So the answer to your question is:
a. There are 18 South American butterflies.
b. There are 12 European butterflies.
I hope this explanation helps! Let me know if you have any further questions.