Question 218487
Ok, begin by assigning a variable to the unknown quantity.
Let x = the number of pounds of nuts worth 0.80 per pound, then (30-x) = the number of pounds of nuts worth $0.50 per pound.  The sum of these two amounts is going to = 30 pounds of nut-mixture worth $0.75 per pound.
These can be expressed algebraically as:
{{{x(0.80)+(30-x)(0.50) = 30(0.75)}}} Simplify and solve for x.
{{{0.8x+15-0.5x = 22.5}}} Combine the x-terms.
{{{03x+15 = 22.5}}} Subtract 15 from both sides.
{{{0.3x = 7.5}}} Divide both sides by 0.3
{{{x = 25}}}
So the grocer will need to mix 25 pounds of nuts worth $0.80 per pound with (30-25 = 5) pounds of nuts worth  $0.50 per pound to obtain 30 pounds of nut-mixture worth $0.75 per pound.