例题：AEAS数学逻辑讲解（一）

　　AEAS数学推理打破了常规数学考试的形式，弱化了数字和公式，而是巧妙的将看似简单的运算与逻辑相结合，立体考察学生的思维逻辑。课窝考试网将陆续分享有关的例题讲解，和大家一起进步。

　　There are two acid solutions S1 and S2, such that S1 contains 50% acid and S2 contains 70% acid. What quantities of S1 and S2 should be mixed to get 10 liters of a solution that contains 54% acid.

　　有S1和 S2两种酸溶液，S1中酸的浓度为50%，S2中酸的浓度为70%.需要多少S1和 S2溶液混合才能得到10升浓度为54%的溶液？

　　Answer:

　　8 liters of S1 and 2 liters of S2

　　Step 1

　　Let the quantities of solutions mixed together be x and y. The first equation, according to the question, is x + y = 10 as their quantities sum up to a total of 10 litres.

　　Step 2

　　The quantity of acid in one litre of the first solution will be equal to 50/100 *1 = 0.5liters

　　Step 3

　　Similarly, the quantity of acid in one litre of the second solution will be equal to 70/100*1=0.7liters

　　Step 4

　　The quantity of acid in one litre of the final mixture is 54/100*1=0.54liters

　　Step 5

　　Since, the first and second solutions are mixed in their respective quantities to 10 litres of the final equation, we can say that x × 0.5 + y × 0.7 = 10 × 0.54

　　or, 0.5x + 0.7y = 5.4

　　Step 6

　　We now have two linear equations in two variables. Let us solve them:

　　x + y = 10

　　or, x = 10 – y ——(1)

　　0.5x + 0.7y = 5.4 ——(2)

　　Substitute the value of x in equation (2)

　　0.5(10 – y) + 0.7y = 5.4

　　or, 5 – 0.5y + 0.7y = 5.4

　　or, -0.2y = -0.4

　　or, y = 2

　　Substitute the value of y in equation (1)

　　x = 10 – 2 = 8

　　Step 7

　　Hence, 8 litres of solution S1 and 2 litres of solution S2 are mixed together to form the given solution.

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