Answer:
18 pounds of cashews are needed.
Step-by-step explanation:
Given;
A manager bought 12 pounds of peanuts for $30.
Price of peanut per pound P = $30/12 = $2.5
Price of cashew per pound C = $5
Price of mixed nut per pound M = $4
Let x represent the proportion of peanut in the mixed nut.
The proportion of cashew will then be y = (1-x), so;
xP + (1-x)C = M
Substituting the values;
x(2.5) + (1-x)5 = 4
2.5x + 5 -5x = 4
2.5x - 5x = 4 -5
-2.5x = -1
x = 1/2.5 = 0.4
Proportion of cashew is;
y = 1-x = 1-0.4 = 0.6
For 12 pounds of peanut the corresponding pounds of cashew needed is;
A = 12/x × y
A = 12/0.4 × 0.6 = 18 pounds
18 pounds of cashews are needed.
