例题:AEAS数学逻辑讲解(一)
- 2018-08-16
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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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