Question 46582
x = pounds of $9 beans
y = pounds of $12 beans
together they add up to 100 pounds
x + y = 100
(income from sales of $9 beans) + (income from sales of $12 beans) = total income
total income = (total pounds of mixture) x (price per pound of mixture)
{{{9x + 12y = 100 * 11.25}}}
{{{x + y = 100}}}
multiply the 2nd equation by 9 and subtract from the 1st
{{{9x + 12y = 100 * 11.25}}}
{{{9x + 9y = 900}}}
{{{12y - 9y = 1125 - 900}}}
{{{3y = 225}}}
{{{y = 75}}} pounds of $12 beans to be sold
{{{x + y = 100}}}
{{{x + 75 = 100}}}
{{{x = 25}}} pounds of $9 beans to be sold
check
{{{9x + 12y = 100 * 11.25}}}
{{{9*25 + 12*75 = 1125}}}
{{{225 + 900 = 1125}}}
{{{1125 = 1125}}}
OK
{{{x + y = 100}}}
{{{25 + 75 = 100}}}
{{{100 = 100}}}
OK