Question 789807
This is a mixture problem involving price and cost.  The target is about finding a price of resulting blend which becomes 5.17 DOLLARS per POUND.


{cost of blend}/{pounds of blend}={price of blend}


Let x = pounds of the 6 dollar a pound coffee
Let y = pounds of the 3.5 dollar a pound coffee


{{{highlight((6x+3.5y)/(150)=5.17)}}} AND {{{highlight(x+y=150)}}}


YES.   TWO Equations.   They are both linear equations.  Work with the ratio equation so it is either easier to use for substitution or so it is in Standard Form:

{{{6x+3.5y=150(5.17)}}}
Subtract 6 of the mass sum equation from this price equation to solve for y:
{{{6x+3.5y-(6x+6y)=150(5.17)-6(150)}}}
{{{-2.5y=150(5.17-6)}}}
{{{2.5y=150(6-5.17)}}}
{{{2.5y=150(0.83)}}}
{{{y=(1/2.5)150(0.83)}}}
{{{y=49.8}}} pounds
Now find the other value higher priced coffee, {{{x=100.2}}}


To nearest pound,
{{{highlight(x=100)}}} pounds, the more expensive coffee
{{{highlight(y=50)}}} pounds, the cheaper coffee