Question 214314
One way to approach these kinds of problems is to write down the amounts of copper (Cu) there are in the different brass alloys. Let x = the amount of the brass with 75.5% Cu.
The amount of amount of Cu in x kgs of this alloy can be expressed as:
{{{x(0.755)}}}kg of Cu.
The amount of Cu in the other 86.3% Cu-brass alloy can be expressed as:
{{{(5250-x)(0.863)}}}kg. of Cu.
The sum of these two amounts is to equal 5250 kg of 80% Cu-brass.
So we can write the equation to find x.
{{{0.755x+0.863(5250-x) = 0.8(5250)}}} Simplify and solve for x.
{{{0.755x+4530.75-0.863x = 4200}}}
{{{-0.108x+4530.75 = 4200}}} Subtract 4530.75 from both sides.
{{{-0.108x = -330.75}}} Divide both sides by -0.108
{{{highlight(x = 3062.5)}}}kg of the brass with 75.5% Cu.