An alloy consists of nickel, zinc, and copper in the ratio 2:7:9. How much alloy can be made with 4.9 lb of zinc and 1.4 lb of nickel?
We need to determine the amount of copper in the alloy using the given ratio. Let's represent the amount of copper as $x$.
Since the ratio of copper to nickel is $9:2$, the ratio of copper to zinc is also $9:2$. Therefore, the ratio of copper to the sum of nickel and zinc is $9:2+7=9:9=1:1$.
Since nickel and zinc are $1.4$ lb and $4.9$ lb respectively, the sum of nickel and zinc is $1.4+4.9=6.3$ lb. So, the amount of copper is also $6.3$ lb.
Therefore, the total amount of the alloy that can be made is $1.4+4.9+6.3=\boxed{12.6}$ lb.
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The ratio of nickel to zinc to copper in the alloy is 2:7:9.
Given that we have 4.9 lb of zinc and 1.4 lb of nickel, we can calculate the amount of copper in the alloy.
The ratio of nickel to zinc is 2:7. So, if we have 4.9 lb of zinc, we have 4.9 * (2/7) lb of nickel.
Since the ratio of nickel to copper is 2:9, we have 4.9 * (2/7) * (9/2) lb of copper.
Calculating this gives us:
Copper = 4.9 * (2/7) * (9/2) = 4.9 * 9/7 = 6.27 lb
Therefore, the amount of alloy that can be made with 4.9 lb of zinc and 1.4 lb of nickel is 4.9 + 1.4 + 6.27 = 12.57 lb.
So, we can make approximately 12.57 lb of alloy.
To find out how much alloy can be made, we need to determine the amount of copper present in the alloy.
Given that the ratio of nickel, zinc, and copper in the alloy is 2:7:9, we can assume that for every 2 parts of nickel, there are 7 parts of zinc and 9 parts of copper.
Let's first find out the total number of parts in the ratio:
2 (parts nickel) + 7 (parts zinc) + 9 (parts copper) = 18 parts
Next, we need to determine the proportion of zinc and nickel compared to the total number of parts:
Proportion of zinc = (7 parts zinc) / (18 total parts)
Proportion of nickel = (2 parts nickel) / (18 total parts)
To calculate the amount of alloy we can make, we'll multiply the proportions by the available quantities of zinc and nickel.
Amount of alloy = (Proportion of zinc) * (available zinc) + (Proportion of nickel) * (available nickel)
Let's plug in the values:
Amount of alloy = (7/18) * 4.9 lb (zinc) + (2/18) * 1.4 lb (nickel)
Calculating this, we have:
Amount of alloy = (7/18) * 4.9 + (2/18) * 1.4
Simplifying the equation further:
Amount of alloy = 1.91 + 0.16
Therefore, the amount of alloy that can be made with 4.9 lb of zinc and 1.4 lb of nickel is approximately 2.07 lb.