An Algebra I test contains 30 questions. Some of the questions are worth 4 points each, and some are worth 2 points each. The total test is worth 100 points. Let f represent the number of questions worth 4 points and t, the number of questions worth 2 points.
Solve the system by elimination to find how many two-point questions the test contains
f + t = 30
4f + 2t = 100
4f + 4t = 120
4f + 2t = 100
2t = 20
t = 10
So, f = 20
To solve the system of equations, we need to set up the equations based on the given information.
Let f represent the number of questions worth 4 points and t represent the number of questions worth 2 points.
From the given information, we know that the total number of questions is 30. This can be represented as the equation:
f + t = 30 --------(1)
We also know that the total points for the test is 100. Since each 4-point question contributes 4 points and each 2-point question contributes 2 points, we can set up the equation:
4f + 2t = 100 --------(2)
Now, we need to solve these two equations using elimination:
Multiply equation (1) by 2 to eliminate t:
2f + 2t = 60 --------(3)
Subtract equation (3) from equation (2) to eliminate t:
(4f + 2t) - (2f + 2t) = 100 - 60
2f = 40
Divide both sides by 2:
f = 20
So, there are 20 questions worth 4 points.
Substitute this value of f into equation (1) to solve for t:
20 + t = 30
Subtract 20 from both sides:
t = 10
Therefore, there are 10 questions worth 2 points on the test.