Out of 42 kids in a class twice as many failed Ela as math,4 failed both. If 7 failed neither, find how many failed each subject.

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M+2M-4+7=42

M=13 failed Math

To solve this problem, we can use a method called the "Principle of Inclusion and Exclusion." Let's break down the given information step by step.

We know that there are 42 kids in the class. We'll use variables to represent the number of students who failed Ela, the number of students who failed Math, and the number of students who failed both subjects.

Let's say the number of students who failed Ela is "x." Since twice as many students failed Ela as Math, we can say that the number of students who failed Math is x/2. Additionally, 4 students failed both subjects.

Now, we need to find the number of students who failed neither subject. We know that 7 students failed neither Ela nor Math. To find this number, we can subtract the total number of students who failed at least one subject from the total number of students in the class.

Total students in the class = 42
Total students who failed at least one subject = x (failed Ela) + x/2 (failed Math) - 4 (failed both)
Total students who failed neither subject = 42 - (x + x/2 - 4)

To find the values of "x" and "x/2," we need to consider the principle of inclusion and exclusion. It states that:

Total students who failed at least one subject = x + x/2 - 4 = 42 - (students who failed neither)

Now, we can solve this equation for "x":

x + x/2 - 4 = 42 - (42 - (x + x/2 - 4))

Simplifying this equation, we get:

3x/2 - 4 = 2x + 2

Solving this equation, we find "x" to be:

3x/2 - 2x = 2 + 4
x/2 = 6
x = 12

Now that we have the value of "x," we can determine the number of students who failed Math:

Number of students who failed Math = x/2 = 12/2 = 6

In summary, 12 students failed Ela, and 6 students failed Math.