Question 190224
Let x = the number of 4-point problems, then (30-x) is the number of 3-point problems.
The total number of points (100) is given by 4x+3(30-x), so...
4x+3(30-x) = 100 Simplify and solve for x.
4x+90-3x = 100 Subtract 90 from both sides.
4x-3x = 10
x = 10
The number of 4-point problems is 10.
The number of 3-point problems is 30-10 = 20.
Check:
4(10)+3(20) = 40+60 = 100 This is the total number of points.
10+20 = 30 This is the total number of problems.