Let the weight percentages of higher and lower price coffee beans in the blend be "a" % and "b" % respectively. So, a+b=100 ··· Eq.1 And one pound of blended beans consists of (a/100) pounds of higher price beans, and (b/100) pounds of lower price beans.
Thus, the price of blended beans per pound can be written as shown below:
5.25(a/100)+3.25(b/100)=4.50 Multiply both sides by 100, getting
5.25a+3.25b=450 From Eq.1, we have: b=100-a Plug this into the equation, getting
5.25a+3.25(100-a)=450 Solve the equation for a, we have:
a=62.5% And from Eq.1, we also have: b=100-a=100-62.5=37.5%
Therefore, the total quantity of higher price beans is: 160x(a/100)=160x(62.5/100)=100 pounds,
and the total quantity of lower price beans is: 160-100=60 pounds.
The answer: She should blend 100 pounds of higher price beans with 60 pounds of lower price beans.