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:
[tex]x+y=70[/tex](number of 2 point questions+number of 4 point questions=total number of questions)
[tex]2x+4y=150[/tex] (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
[tex]x+y=70 , 2x+4y =150[/tex]
We will solve one of these equations.
[tex]x+y=70[/tex]
[tex]x=70-y[/tex]
Next, we will substitute the other equation with this solution.
[tex]2* (70-y) +4y =150\\140-2y+4y=150\\2y=10\\y=5[/tex]
Use this solution to find x.
[tex]x+y=70\\x+5=70\\x=65[/tex]
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.
[tex]46*2+4y=100\\92=4y=100\\4y=8\\y=2[/tex]
So, she answered 2 questions correctly.
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