Question 534086
Let x be the amount (in grams) of the 70% alloy.
Let y be the amount (in grams) of the 20% alloy.
We want
{{{x+y=500}}} and
{{{0.7x+0.2y=0.55*500}}} or {{{0.7x+0.2y=275}}}
Now we have a system of linear equations:
{{{x+y=500}}} and
{{{0.7x+0.2y=275}}}
We can solve by elimination like this:
multiply the first equation times -0.2 to get
{{{-0.2x-0.2y=-100}}}
and add it to the second equation to eliminate y, getting
{{{0.5x=175}}} so {{{x=175/0.5=340}}}
Plugging that value back into
{{{x+y=500}}} we get
{{{340+y=500}}} so {{{y=500-340=150}}}