Banknotes

Eva deposited 7800 USD in 50 banknotes in the bank.
They had a value of 100 USD and 200 USD.
How many were they?

Correct answer:

a =  22
b =  28

Step-by-step explanation:


a+b = 50
100a+200b = 7800

a+b = 50
100·a+200·b = 7800

a+b = 50
100a+200b = 7800

Pivot: Row 1 ↔ Row 2
100a+200b = 7800
a+b = 50

Row 2 - 1/100 · Row 1 → Row 2
100a+200b = 7800
-b = -28


b = -28/-1 = 28
a = 7800-200b/100 = 7800-200 · 28/100 = 22

a = 22
b = 28

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