AEAS是Australian Education Assessment Service, 澳大利亚教育评估服务机构的简称,成立于1985年，30年来一直致力于为准备进入澳大利亚初高中学习的国际学生提供高水平的综合性测试服务。今天小编为大家带来关于AEAS数学考试例题介绍，希望同学们掌握其中的运算和逻辑思维，下面就和小编一起看看吧。
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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