Question

How many pounds of peanuts costing $3.60 a pound should be mixed with 4 pounds of cashews costing $4.50 a pound to obtain a mixture costing $3.50 a pound?

Answer 1

8 pounds of peanuts has to be mixed with cashews

SOLUTION:

Given that , we have to find how many pounds of peanuts costing $3.00 a pound should be mixed with 4 pounds of cashews costing $4.50 a pound to obtain a mixture costing $3.50 a pound?

Now, let the weight of peanuts be n pounds.

Then, according to given information,  

cost of m pounds of peanuts = 3.60m

cost of n pounds of cashews = 4 x 4.50 = $ 18  

now, total weight of mixture = n + 4

then, total cost of mixture = 3.50(n + 4)

now we also know that, total cost of mixture = cost of peanuts + cost of cashews

3.50(n + 4) = 3n + 18

3.50n + 14 = 3n + 18

3.50n – 3n = 18 – 14

0.5n = 4

n = 8

Hence, 8 pounds of peanuts has to be mixed with cashews.