Your teacher is giving you a test worth 100 points containing 40 questions. There are 2-point and 4-point questions on the test. How many of each type are there.
dealing w/-subst. and elimin.
let number of 2 pointers be x, then number of 4pointers is y
so x+y = 40
2x + 4y = 100
take it from there
To determine how many of each type of question there are, we can use the method of substitution and elimination.
Let's assume the number of 2-point questions is x, and the number of 4-point questions is y.
We are given two pieces of information:
1. The total number of questions is 40: x + y = 40
2. The total point value of the test is 100: 2x + 4y = 100
Using the substitution method, we can solve one equation for one variable and substitute it into the other equation.
From the first equation, we can express x in terms of y: x = 40 - y
Substituting the value of x in the second equation, we get:
2(40 - y) + 4y = 100
80 - 2y + 4y = 100
2y = 100 - 80
2y = 20
y = 10
Therefore, there are 10 four-point questions on the test.
Substituting this value of y in the first equation, we can find x:
x + 10 = 40
x = 40 - 10
x = 30
Hence, there are 30 two-point questions on the test.
In summary, there are 30 two-point questions and 10 four-point questions on the test.