Question

A grocer bought some walnuts for 45¢ per pound and some pecans for 60¢ per pound. He wants to mix the pecans and walnuts together to form a 90 pound mixture to sell at 55 cents per pound. If x represents the pounds of walnuts used in the mixture, which expression would represent the total cost of the pecans used in the mixture?

Answer 1

Cost of walnuts = 45 cents per pound
Weight of walnuts in mixture = x pounds

So, total cost of walnuts in the mixture = 45x
This gives the cost in cents. The cost in dollars will be = 0.45x

Cost of pecans = 60 cents per pound

Since total weight of the mixture is 90 pounds. The weight of pecans in the mixture will be (90 - x) pounds.

So, total cost of pecans in the mixture will be = 60 (90 - x)
This gives the cost in cents, the cost in dollars will be = 0.6 (90 - x)

x pounds of walunts and (90-x) pounds of pecans are mixed to produce a mixture to sell at 55 cents per pound. So,we can set up the equation for this case as:

Cost of Walnuts + Cost of Pecans = Cost of Mixture


`0.45x+(90-x)*0.60=90(0.55)`

Using this equation, we can find the weight of walnuts, using x we can also find the weight of pecans. From weights we can then calculate the cost of walnuts and pecans used in the mixture.