Answer:
There were 12 questions worth 3 points
Step-by-step explanation:
Let x = 2 point questions
let y = 3 point questions
What we know:
x + y = 20 (questions)
so to solve for x we tweak our equation:
x = 20 - y
Now we need an equation to explain out question set up:
2x (2 point questions)
3y (2 point questions)
2x + 3y = 52 (52 being our total possible points)
Now we take our x = 20 - y and substitute it into our 2x + 3y = 52 equation.
2(20 - y) + 3y = 52
Next we distribute the 2 through the parenthesis:
40 - 2y + 3y = 52
Now, gather the like terms:
40 + y = 52
Subtract 40 from both sides:
y = 12
Revisit x + y = 20 and sub 12 in for Y:
x + 12 = 20
x = 8
8 2-point questions would be 16 points
12 3-point questions would be 36 points
16 + 36 = 52 (which matches the max value of our test)
