Answer:
65 problems were solved correctly, 35 incorrecly.
Step-by-step explanation:
1. Data:
Total answers= 100
50 cent = $0.50 for each correct answer
-30 cent = -$0.30 for each incorrect answer
Net reward= $22.00
2. Define Variables:
x= Correct answers
y= Incorrect answers
3. Formulate the Equations
Total number of answers (Eq 1)
[tex]x+y=100\\y=100-x[/tex]
Net reward (Eq 2)
[tex]0.50*x-0.30*y=22.00[/tex]
4. Solve by replaccing the Eq 1 in Eq 2 as follows:
[tex]0.50*x-0.30*y=22.00\\0.50*x-0.30*(100-x)=22.00[/tex]
5. Apply distrivutive property and operate:
[tex]0.50x-(0.30*100)+(0.30*x)=22.00\\0.50x-30.00+0.30x=22.00[/tex]
6. Separate numbers and variables on each side of the equation and solve
[tex]0.50x+0.30x=22.00+30.00\\0.80x=52.00[/tex]
7. Solve x
[tex]x=\frac{52.00}{0.8} \\x=65[/tex]
Now you know that correct answers are equal to 65
8. Find Incorrect Answers with Eq 1.
[tex]y=100-x\\y=100-65\\y=35[/tex]
Now you know that incorrect answers are equal to 35
9. Answer
65 problems were solved correctly, 35 incorrecly.
