# Originally 7182

Together, Peter and Jano had 52,000 stamps in their collection. To compete with their friend, they must have 56700 marks. They agreed that Peter would increase his collection by 8 percent and Janko would give 10 percent more than he has. How many marks did each of them have originally?

j =  27000
p =  25000

## Step-by-step explanation:

p+j = 52000
1.08 p + 1.10 j = 56700

p+j = 52000
1.08·p + 1.10·j = 56700

j+p = 52000
1.1j+1.08p = 56700

Pivot: Row 1 ↔ Row 2
1.1j+1.08p = 56700
j+p = 52000

Row 2 - 1/1.1 · Row 1 → Row 2
1.1j+1.08p = 56700
0.02p = 454.55

p = 454.54545448/0.01818182 = 25000.00000022
j = 56700-1.0800000000017p/1.1 = 56700-1.08 · 25000.00000022/1.1 = 26999.99999978

j = 27000
p = 25000

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