Question

An alloy is composed of nickel, zinc, and copper in a 7:2:9 ratio. How many kilograms of each metal is needed to make 3.8 kg of this alloy?

Answer 1

To create the alloy, 1.4777 kg of nickel, 0.4222 kg of zinc, and 1.8999 kg of copper are needed to maintain the given 7:2:9 ratio in a total mass of 3.8 kg.

Step-by-step explanation:

To make an alloy with a nickel, zinc, and copper ratio of 7:2:9 to total 3.8 kg, we need to determine the amount of each metal in kilograms. First, we add the parts of the metals together: 7 (nickel) + 2 (zinc) + 9 (copper) = 18 parts in total. We then calculate the weight of each part by dividing 3.8 kg by the total number of parts, which is 3.8 kg ÷ 18 parts = 0.2111 kg per part. Next, we multiply the number of parts for each metal by the weight of one part: nickel (7 parts) = 7 × 0.2111 kg = 1.4777 kg, zinc (2 parts) = 2 × 0.2111 kg = 0.4222 kg, and copper (9 parts) = 9 × 0.2111 kg = 1.8999 kg. This gives us the required amounts of each metal to create the alloy.

Answer 2

Ni : Zn: Cu = 7:2:9 =7x : 2x : 9x

7x+2x+9x = 3.8
18x=3.8
x=3.8/18=1.9/9≈0.21

Ni: 7x=7*0.21=1.47 ≈1.5 kg
Zn: 2x=2*0.21=0.42≈0.4 kg
Cu: 9x=9*0.21=1.89 ≈1.9 kg

Check 1.5+0.4+1.9 =3.8 True