Competition 4729

The teacher submitted ten tasks during the competition. Students will receive 5 points for each correctly solved problem; 3 points will be deducted for an incorrect solution. How many math problems did the student solve correctly if he finally got 34 points?

Correct answer:

d =  8

Step-by-step explanation:


d+z=10
5d -3z = 34

d+z=10
5·d -3·z = 34

d+z = 10
5d-3z = 34

Pivot: Row 1 ↔ Row 2
5d-3z = 34
d+z = 10

Row 2 - 1/5 · Row 1 → Row 2
5d-3z = 34
1.6z = 3.2


z = 3.2/1.6 = 2
d = 34+3z/5 = 34+3 · 2/5 = 8

d = 8
z = 2

Our linear equations calculator calculates it.



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