An alloy of copper and aluminum has 40% copper. An alloy of Copper and Zinc has Copper and Zinc in the ratio 2:7. These two alloys are mixed in such a way that in the overall alloy, there is more aluminum than Zinc, and copper constitutes x% of this alloy. What is the range of values x can take?  Choose the correct choice from the following options.
A) 30% ≤ x ≤ 40% B) 32.5% ≤ x ≤ 40% C) 32.5% ≤ x ≤ 42% D) 33.33% ≤ x ≤ 40% E) 33.33 % ≤ x ≤ 42%
The maximum aluminium you can have is when you mix copper and aluminium alloy (say alloy A) with infinitesimally small amount of copper and zinc alloy (alloy B). In that case, you will have almost 40% of copper in the mix (because alloy A has 40% of copper). So x% &lt; 40%.   Minimum case:   60% of alloy 30% ≤ x ≤ 40% &gt; (7/9) of alloy B   30% ≤ x ≤ 40%/B &gt; 35/27   If the two alloys are mixed in this ratio, the copper concentration will be:   Using weighted average:   Cavg = (2/5 * 35 + 2/9 * 27)/(35 + 27)   Cavg = (14 + 6)/62= 20/62 = 32.26% (rounded to 2 decimal places)   So x% &gt; 32.26%   30% ≤ x ≤ 40%nswer: 32.26 &lt; x &lt; 40   30% ≤ x ≤ 40%NSWER:30% ≤ x ≤ 40%
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An alloy of copper and aluminum has 40% copper. An alloy of Copper and Zinc has Copper and Zinc in the ratio 2:7. These two alloys are mixed in such a way that in the overall alloy, there is more aluminum than Zinc, and copper constitutes x% of this alloy. What is the range of values x can take?