Sweets

3 chocolate and 7 cakes cost 85, - CZK. 2 chocolates and 6 cakes cost 86, - CZK. How much is 5 chocolates and 9 cakes?

I wonder how to get the result, but only by logic without the use of a system of equations

Correct result:

x =  123 Kč

Solution:

3a + 7b = 85
6a + 2b = 86
5a + 9b = x

3•a + 7•b = 85
6•a + 2•b = 86
5•a + 9•b = x

3a+7b = 85
6a+2b = 86
5a+9b-x = 0

a = 12
b = 7
x = 123

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