In the fourth year of a school. There were 156 students who took both mathematics and science. They all passed at least one subject and 75 passed both subjects. If twice as many passed science as passed Mathematics, find how many passed in mathematics only.
If x passed math, then we have
x + 2x - 75 = 156
Find x, and then x-75 passed math only
To find the number of students who passed mathematics only, we first need to determine the total number of students who passed mathematics.
Let's use the given information and start solving step by step:
1. We are told that 156 students took both mathematics and science, and 75 students passed both subjects. This means that the number of students who took mathematics only is given by:
Number of students who took mathematics only = Total students who took mathematics - Number of students who took both subjects
2. We are also given that twice as many students passed science as passed mathematics. So, let's assign a variable to represent the number of students who passed mathematics. Let's call it 'x'.
Number of students who passed science = 2 * x
3. Now, according to the information given, the total number of students who passed at least one subject is 156. This implies that the sum of students who passed mathematics only and those who passed both subjects is equal to 156. So, we can form the equation:
x + 75 = 156
4. Rearrange the equation to solve for x:
x = 156 - 75
x = 81
Therefore, the number of students who passed mathematics only is 81.