160 kg of an alloy of copper and aluminium contains 55 percent of aluminium. How much aluminium must be melted into it to make the alloy contain 70 percent of alluminium
To solve this problem, we need to determine the amount of aluminum to be melted into the alloy. Here's how we can calculate it:
Step 1: Find the amount of aluminum initially present in the alloy.
We are given that the alloy contains 55% aluminum and weighs 160 kg. To find the amount of aluminum, we multiply the total weight by the percentage of aluminum:
Weight of aluminum = 55% * 160 kg = 0.55 * 160 kg = 88 kg
Step 2: Find the new total weight of the alloy after adding more aluminum.
The question asks us to make the alloy contain 70% aluminum. Let's assume we need to add "x" kilograms of aluminum. Therefore, the new total weight will be 160 kg (existing alloy weight) + x kg (additional aluminum).
Step 3: Set up an equation using the following relationship:
Weight of new aluminum = Total weight of new alloy * Percentage of aluminum
We can now substitute the values we know into the equation:
x kg = (160 kg + x kg) * 70%
Step 4: Solve the equation for x.
Let's solve for x:
x = (160 kg + x kg) * 0.7 (Dividing both sides by 100%)
x = 0.7 * (160 kg + x kg) (Distributing 0.7)
x = 112 kg + 0.7x (Removing brackets)
0.3x = 112 kg (Subtracting 0.7x from both sides)
x = 112 kg / 0.3 (Dividing both sides by 0.3)
x ≈ 373.33 kg
Therefore, approximately 373.33 kg of aluminum must be melted into the alloy to make it contain 70% aluminum.
let the amount of aluminum added be x kg
.55(160) + x = .7(160+x)
88 + .55x + x = 112 + .7x
.85x = 24
x = appr 28.24 kg