160 kg of alloy of copper and aluminium contains 55 percent of aluminium.how much aluminium must be melted into it to make aluminium 70 percent.
.55*160 + x = .70(160+x)
If one plane is flying at 40 mph while another is flying at 100 mph, and they are 200 miles apart and flying directly towards each other, how long will it take them to meet?
To find out how much aluminium needs to be melted into the alloy, we can follow these steps:
Step 1: Determine the amount of aluminium in the initial alloy.
Given that the alloy contains 160 kg of material and 55% of it is aluminium, we can calculate the amount of aluminium in the alloy using the formula:
Amount of Aluminium = (Percentage of Aluminium / 100) * Total weight of alloy
Amount of Aluminium = (55 / 100) * 160 kg
= 0.55 * 160 kg
= 88 kg
Therefore, there are 88 kg of aluminium in the initial alloy.
Step 2: Determine the new total weight of the alloy after adding more aluminium.
Assuming x kg of aluminium is added to the alloy, the new total weight of the alloy becomes:
New Total Weight = Initial Weight + Added Aluminium
New Total Weight = 160 kg + x kg
Step 3: Determine the new percentage of aluminium required.
We want the final percentage of aluminium to be 70%. To calculate how much aluminium is in the new alloy, we need to multiply the new total weight of the alloy by the new percentage of aluminium. We can set up the equation as follows:
Amount of Aluminium = (Percentage of Aluminium / 100) * New Total Weight
0.70 * (160 kg + x kg) = Amount of Aluminium
Step 4: Solve the equation for x to find out how much aluminium needs to be added.
Substitute the value of the amount of aluminium we found in step 1:
0.70 * (160 kg + x kg) = 88 kg
Multiply both sides of the equation by (160 kg + x kg):
0.70 * (160 kg + x kg) = 88 kg * (160 kg + x kg)
Expand and simplify:
112 kg + 0.70x kg = 88 kg * (160 kg + x kg)
112 kg + 0.70x kg = 14080 kg + 88 kgx kg
Rearrange and combine like terms:
0.70x kg - 88 kgx kg = 14080 kg - 112 kg
-87.30x kg = 13968 kg
Divide both sides by -87.30 kg to solve for x:
x kg = 13968 kg / -87.30 kg
x kg ≈ -159.9 kg
Since we can't have a negative mass of aluminium, it is not possible to add a negative amount of aluminium to the alloy. Therefore, we cannot achieve a 70% aluminium composition with the given amount of alloy.