SOLUTION: 5 kg of heavy water of unknown isotopic purity, when added to 10 kg of heavy water of different grade produced a mixture of isotopic purity of 80% by weight. when 2 kg of the first

Question 1082568: 5 kg of heavy water of unknown isotopic purity, when added to 10 kg of heavy water of different grade produced a mixture of isotopic purity of 80% by weight. when 2 kg of the first sample is added to 3 kg of the second sample, the resulting mixture had an isotopic purity of 78% by weight. calculate the isotopic purities of the two samples.
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
5x + 10y = 12 (15(0.8)) multiply both sides times 2
2x + 3x = 3.9 (5(0.78)) multiply both sides times -5 and add to the other equation
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
10x + 20y = 24
-10x + -15y = -19.5
-------------------
0x + 5y = 4.5
5y = 4.5
y = 0.9 = 90%
plug this into one of the original equations to solve for x.
5x + 10(0.9) = 12
= 0.6
try the other equation if you want to double-check:
2x + 3(0.9) = 3.9
= 0.6
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