One fourth of class takes French.
One half takes Latin
One third as many take Japanese as Latin students. There are 8 students taking Japanese.
***no students take more than one language
How many students take French?12
How many students take Latin? 24
How many students are in the class? 48
***
To determine the number of students taking each language and the total number of students in the class, we follow these steps:
Step 1: Calculate the number of students taking Japanese. According to the given information, the number of students taking Japanese is one third of the number of students taking Latin, which is 8. Therefore, the number of students taking Japanese is 8.
Step 2: Calculate the number of students taking Latin. According to the given information, half of the class takes Latin. So, we can set up the equation: (1/2) * Total number of students = Number of students taking Latin. Plugging in the given value for the number of students taking Latin (24), we can solve for the total number of students in the class. Simplifying the equation gives us: (1/2) * Total number of students = 24. Multiplying both sides by 2, we find that the total number of students is 48.
Step 3: Calculate the number of students taking French. According to the given information, one-fourth of the class takes French. So, we can set up the equation: (1/4) * Total number of students = Number of students taking French. Plugging in the given value for the number of students taking French (12) and the total number of students (48) that we found in step 2, we can solve for the missing value. Simplifying the equation gives us: (1/4) * 48 = 12. Therefore, the number of students taking French is 12.
In summary, based on the given information, 12 students take French, 24 students take Latin, and the total number of students in the class is 48.