Mixing

If we mix 5 kg of goods of one kind and 3 kg of the second one, the resulting mixture costs 16.50 EUR/kg. If these quantities are mixed in reverse - the first three kilograms and 5 kilograms of the second cost of the mixture is 18.50 EUR/kg. What is the price of one kg of goods of every kind?

Correct answer:

a =  13 12 = 27/2 Eur/kg
b =  21 12 = 43/2 Eur/kg

Step-by-step explanation:


(5a+3b)/(5+3) = 16.50
(3a+5b)/(5+3) = 18.50


(5·a+3·b)/(5+3) = 16.50
(3·a+5·b)/(5+3) = 18.50

0.625a+0.375b = 16.5
0.375a+0.625b = 18.5

Row 2 - 0.375/0.625 · Row 1 → Row 2
0.63a+0.38b = 16.5
0.4b = 8.6


b = 8.6/0.4 = 21.5
a = 16.5-0.375b/0.625 = 16.5-0.375 · 21.5/0.625 = 13.5

a = 27/2 = 13.5
b = 43/2 = 21.5

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