The number of 144 students who registered for mathematics, physics, and chemistry in an examination are shown in the Venn diagram. How many registered for physics and mathematics?
144 = 42 - x + 30 - x + 34 + 4x + 3x + 6 + x + 2x
144 = 112 + 8x
8x = 144 - 112 = 32
x = 4.
The number of students that registered for physics and mathematics = 4x + 2x = 4 x 4 + 2 x 4 = 24.
