Answer:
65 two-point questions, and 5 four-point questions.
Emma answered 2 four-point questions.
Step-by-step explanation:
1. Assigning variables and writing equations
We will set the number of 2 point questions as "x" and number of 4 point questions as "y"
We know that:
x+y=70 (number of 2 point questions+number of 4 point questions=total number of questions)
2x+4y=150 (number of points that a two point question is worth*number of two point questions+number of points that a four point question is worth*number of four point questions=total points on test)
2. Combining equations
x+y=70, 2x+4y=150
We will solve one of these equations.
x+y=70
x=70-y
Next, we will substitute the other equation with this solution.
2*(70-y)+4y=150
140-2y+4y=150
2y=10
y=5
Use this solution to find x.
x+y=70
x+5=70
x=65
We found that there are 65 two-point questions, and 5 four-point questions.
3. Finding Emma's test results
In this case, we know how many two-point questions she answered. So, we will only be using one variable in this equation, which is y.
46*2+4y=100
92+4y=100
4y=8
y=2
So, she answered 2 questions correctly.
