The document discusses mixing two alloys - one with 40% copper and aluminum, and another with copper and zinc in a 2:7 ratio. These alloys are mixed such that there is more aluminum than zinc in the overall alloy. The percentage of copper in the overall alloy is represented by x. Through analyzing limiting cases where the amounts of one alloy are minimized or maximized, it is determined that the range of possible values for x is between 32.25% and 40%.

1. Mixtures

2. Mixtures
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?
(a) 30% < x < 40% (b) 32.5% < x < 42%
(c) 33.33% < x < 40% (d) 32.5% < x < 40%

3. Mixtures
Alloy 1 Copper Aluminium
2x 3x
Alloy 2 Copper Aluminium
2y 7y
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?

4. Mixtures
If aluminium and zinc have to be equal, 3x = 7y. The simplest case
occurs at the LCM, when both aluminium and zinc are 21kg.
Alloy 1 Copper Aluminium
14 21
Alloy 2 Copper Aluminium
6 21
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?

5. Mixtures
Even a gram of Alloy 1 above this level would mean that there is
more aluminium than zinc in the total alloy. So, this table is a limit on
the percentages of different metals.
The percentage of copper in the total alloy would be
(14 + 6) × 100/62 = 32.25%.
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?

6. Mixtures
On the other hand, if we want more aluminium than zinc, we can use
tons and tons of Alloy 1, and only a microgram of Alloy 2.
The quantity of Alloy 2 can be made so small that its presence can be
almost neglected, as it will have as good as zero impact on the
overall percentage of copper.
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?

7. Mixtures
This is another extreme case, in which copper will have 40% weight
in the alloy 2/(2+3).
Thus, the percentage of copper ranges from 32.25% to 40% in this
alloy.
Answer Choice (a)
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?

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