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Question
A chemist has one solution which is 50% acid and another solution which is 25% acid. How much each should be mixed to make 10 litres of a 40% acid solution? (Use Cramer’s rule to solve the problem).
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Solution
Let two solutions x and y
x + y = 10 .........(1)
0.25x + (0.50)y = (0.40) .........(2)
(2) × 100 ⇒ 25x + 50y = 400
(2) ÷ 5 ⇒ 5x + 10y = 80 .........(3)
Δ = `|(1, 1),(5, 10)|` = 10 – 5 = 5 ≠ 0
Δx = `|(10, 1),(80, 10)|` = 100 – 80 = 20
Δy = `|(1, 10),(5, 80)|` = 80 – 50 = 30
x = `Delta_x/Delta = 20/5` = 4 (litres of 25% solution)
y = `Delta_y/Delta = 30/5` = 6 (litres of 50% solution)
x = 4, y = 6
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