In Class A there are 80 the Boy to Girl ratio is 3 to 5. In Class B the boy to girl ratio is 3 to 2. If the 2 classes combined have an equal number o fboys and girls how many students are in class B?
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To solve this problem, we need to first determine the number of boys and girls in Class A, and then calculate the number of boys and girls in Class B. Let's break it down step by step:
Step 1: Determine the number of boys and girls in Class A.
- In Class A, the boy to girl ratio is 3 to 5.
- This means that for every 3 boys, there are 5 girls.
- To find the total number of students in Class A, we need to determine the common multiplier for 3 and 5. In this case, it would be 15 (3 × 5 = 15).
- So, for every 3 boys, there are 5 girls, and for every 15 students, there are 8 boys and 5 girls.
- Now we know that the total number of students in Class A is 15.
Step 2: Calculate the number of boys and girls in Class B.
- In Class B, the boy to girl ratio is 3 to 2.
- This means that for every 3 boys, there are 2 girls.
- Since we know that the total number of students in Class A is 15, the combined total number of boys and girls in both classes is also 15.
- We can set up a proportion using the ratio of boys to girls in Class B: 3/2 = x/y, where x represents the number of boys and y represents the number of girls in Class B.
- To solve for x and y, we can cross-multiply: 3y = 2x.
- Since the number of students in Class B is equal to the number of students in Class A (15), the sum of x and y is also 15. Therefore, x + y = 15.
- We have two equations now: 3y = 2x and x + y = 15.
Step 3: Solve the system of equations.
- We have two equations: 3y = 2x and x + y = 15.
- To solve this system of equations, we can use substitution.
- From the second equation, we can isolate x to get x = 15 - y.
- Substitute x in the first equation: 3y = 2(15 - y).
- Simplify the equation: 3y = 30 - 2y.
- Combine like terms: 5y = 30.
- Solve for y: y = 30/5 = 6.
- Now substitute the value of y back into the second equation to find x: x + 6 = 15.
- Solve for x: x = 15 - 6 = 9.
Step 4: Determine the number of students in Class B.
- From the calculations above, we found that there are 9 boys and 6 girls in Class B.
- The number of students in Class B is the sum of the boys and girls: 9 + 6 = 15.
Therefore, there are 15 students in Class B.