Testing

Students in high school have 10 points for each correctly solved problem. Five points are deducted for each wrong answer. After solving 20 problems, student Michael had 80 points. How many problems did he solve correctly, and how many were wrong?

Final Answer:

a =  12
b =  8

Step-by-step explanation:


a+b = 20
10a - 5b = 80

a+b = 20
10·a - 5·b = 80

a+b = 20
10a-5b = 80

Pivot: Row 1 ↔ Row 2
10a-5b = 80
a+b = 20

Row 2 - 1/10 · Row 1 → Row 2
10a-5b = 80
1.5b = 12


b = 12/1.5 = 8
a = 80+5b/10 = 80+5 · 8/10 = 12

a = 12
b = 8

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