Why did the math book go to the therapist?
Because it had too many problems!
Now, let's solve this problem using a Venn diagram!
Let's represent the students who like mathematics and science as "M" and "S", respectively.
According to the information given, the ratio of students who like mathematics and science is 4:5. So, we'll divide the overlapping region into two parts, one representing only mathematics (M) and the other representing only science (S).
We are also given that 10 students like both subjects and 15 students like none. Let's fill in those numbers on our diagram.
M
_
| | _
S | | | |
|_|___|_|
Now, let's do some calculations.
The total number of students who like mathematics and science is 4x + 5x = 9x, where x is a constant.
The total number of students who like only mathematics is 4x - 10 (subtracting the 10 students who like both from the mathematics total).
The total number of students who like only science is 5x - 10 (subtracting the 10 students who like both from the science total).
We are also given that 15 students like none. So, we need to subtract this from the total number of students.
Therefore, the number of students who like only mathematics is (4x - 10) - 15 = 4x - 25 ,
and the number of students who like only science is (5x - 10) - 15 = 5x - 25.
Unfortunately, without knowing the value of x, we can't determine the exact number of students who like only mathematics or science. We can only express them in terms of x, leaving as an algebraic expression.