Question 719979
Summary of given information:
First alloy: 15% Gold, 15% Lead.
Second alloy: 40% Gold, 30% Lead.
WANT NEW ALLOY containing 80.5 grams Gold and 76.5 grams Lead.


Let x = grams of first alloy
Let y = grams of second alloy


Account for Gold:  {{{0.15x+0.40y=80.5 }}}
Account for Lead:  {{{0.15x+0.30y=76.5}}}

Those two, when multiplied by 100 and then divided by 5 give the equivalent system,

{{{highlight(3x+8y=1610)}}}
{{{highlight(3x+6y=1530)}}}


In that form, the second equation can be subtracted from the first equation and the result solved for y, giving the grams of the "second alloy" to use.  Next, use either equation of this system to find the value of x, the "first alloy" to use.