Marble game distribution

Paul, Isaac, and Kurt played bullets. They had a total of 25 marbles. Palo had 6 more bullets than Kurt at the start. Then Isaac won 8 bullets from Paul, and thus Isaac had the same number of bullets as Kurt. How many marbles does Pal have left?

Final Answer:

x =  7

Step-by-step explanation:


p+i+k = 25
p = 6+k
i+8 = k
x = p-8

i+k+p = 25
k-p = -6
i-k = -8
p-x = 8

Row 3 - Row 1 → Row 3
i+k+p = 25
k-p = -6
-2k-p = -33
p-x = 8

Pivot: Row 2 ↔ Row 3
i+k+p = 25
-2k-p = -33
k-p = -6
p-x = 8

Row 3 - 1/-2 · Row 2 → Row 3
i+k+p = 25
-2k-p = -33
-1.5p = -22.5
p-x = 8

Row 4 - 1/-1.5 · Row 3 → Row 4
i+k+p = 25
-2k-p = -33
-1.5p = -22.5
-x = -7


x = -7/-1 = 7
p = -22.5/-1.5 = 15
k = -33+p/-2 = -33+15/-2 = 9
i = 25-k-p = 25-9-15 = 1

i = 1
k = 9
p = 15
x = 7

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