Question 127588
(price/lb cashews)x(lbs cashews) + (price/lb pecans)x(lbs pecans)
divided by (lbs of cashews and pecans)
= (price per lb of mixture)
Let {{{c}}} = pounds of cashews needed
Let {{{p}}} = pounds of pecans needed
{{{(4.5c + 6.5p) / (p + c) = 5.85}}}
{{{c + p = 40}}}
{{{p = 40 - c}}}
{{{(4.5c + 6.5p) / (p + c) = 5.85}}}
{{{(4.5c + 6.5(40 - c)) / 40 = 5.85}}}
{{{4.5c + 260 - 6.5c = 40*5.85}}}
{{{-2c = 234 - 260}}}
{{{-2c = -26}}}
{{{c = 13}}}
{{{p = 40 - c}}}
{{{p = 27}}}
13 pounds of cashews and 27 pounds of pecans are needed
check:
{{{(4.5c + 6.5p) / 40 = 5.85}}}
{{{(4.5*13 + 6.5*27) / 40 = 5.85}}}
{{{(58.5 + 175.5) / 40 = 5.85}}}
{{{234/40 = 5.85}}}
{{{234 = 5.85*40}}}
{{{234 = 234}}}