160 kg of alloy contains 55 percent aluminium. How much alluminium should be added to make it 70 percent
If x kg are added, then we have
.55*160 + 1.00x = .70(160+x)
To determine the amount of aluminum that needs to be added to the existing alloy, we can follow these steps:
Step 1: Calculate the current amount of aluminum in the alloy.
The alloy contains 55% aluminum, which means that 55% of the total weight is aluminum.
So, the current amount of aluminum in the alloy is:
55% of 160 kg = 0.55 * 160 kg = 88 kg
Step 2: Determine the desired final weight of the alloy.
In order to achieve a 70% aluminum content, the total weight of the alloy needs to remain constant.
Therefore, the desired final weight of the alloy will also be 160 kg.
Step 3: Calculate the required amount of aluminum to be added.
Let's assume x kg of aluminum needs to be added.
The equation can be set up as follows:
(88 kg + x kg) / 160 kg = 70%
Step 4: Solve for x.
To solve for x, we can multiply both sides of the equation by 160 kg:
88 kg + x kg = 0.70 * 160 kg
Now, subtract 88 kg from both sides to isolate x:
x kg = 0.70 * 160 kg - 88 kg
Simplifying the right side of the equation:
x kg = 112 kg - 88 kg
x kg = 24 kg
Therefore, 24 kg of aluminum should be added to the alloy to achieve a 70% aluminum content.