Question

Mixed nuts which cost $8/lb are made by combining walnuts which cost $12/lb with peanuts which cost $5/lb. Write an equation to find the number of pounds of walnuts and peanuts required to make 14 lb of mixed nuts.

a) 12w+5p=14
b) 8w+12p=14
c) 12w+5p=112
d) 5w+12p=14

Answer 1

The correct equation to find the number of pounds of walnuts and peanuts needed to make 14 lb of mixed nuts, given the costs of walnuts at $12/lb and peanuts at $5/lb, is '12w + 5p = 112'. Here 'w' represents the weight of walnuts and 'p' for peanuts.

Step-by-step explanation:

The student is required to write an equation to determine the number of pounds of walnuts and peanuts needed to make 14 lb of mixed nuts at a cost of $8/lb, with the given prices of walnuts as $12/lb and peanuts as $5/lb. To formulate this equation, let's designate w as the number of pounds of walnuts and p as the number of pounds of peanuts needed. Since the total weight of the mixed nuts is 14 lb, we have the equation w + p = 14. Additionally, the total cost equation comes from multiplying the quantity by the respective cost and summing for the mixed nuts: (12*w) + (5*p) = 14*8 (since $8/lb for 14 lb). Simplifying this, we get 12w + 5p = 112, which corresponds to option (c).