A quiz had only 3-point questions and four-point questions. The best possible score is 100, and there are 29 questions. How many 4-point questions are there?
number of 4 point questions --- x
number of 3 point questions --- 29-x
solve for x
4x + 3(29-x) = 100
4x+3(29-x)=100
4x+87-3x=100
87+x=100
x=13
13 questions
:)
To solve this problem, let's use algebra.
Let's assume that the number of 3-point questions is represented by "x", and the number of 4-point questions is represented by "y".
We know there are 29 questions in total, so we can create an equation:
x + y = 29 ---(Equation 1)
We also know that the maximum possible score is 100, which means the sum of the points from the 3-point questions (3x) and the sum of the points from the 4-point questions (4y) must equal 100:
3x + 4y = 100 ---(Equation 2)
Now we have a system of equations (Equation 1 and Equation 2) that we can solve simultaneously to find the values of "x" and "y".
Let's solve the system:
Multiplying Equation 1 by 3, we get:
3x + 3y = 87 ---(Equation 3)
Subtracting Equation 3 from Equation 2, we get:
3x + 4y - (3x + 3y) = 100 - 87
Simplifying further:
y = 13
Therefore, there are 13 four-point questions.