A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per
pound and cashews cost $6.50 per pound, how many pounds of each should he use? Let p = pounds of peanuts and let c = pounds of cashews. Write a system of equations that could be used to solve the problem.
The grocer wants to make a 10 pound mixture p - pounds of peanuts c - pounds of cashews therefore the total pounds should be equal to 10 pounds p + c = 10 -----> 1) the cost for ; peanuts - 4.00 per pound * p pounds = 4p cashews - 6.50 per pound * c pounds = 6.5c the price of 10 pounds mixture = 4.75 per pound * 10 pounds = 47.5 4p+6.5c = 47.5 ---> 2)
to solve for p and c lets use simultaneous equations p + c = 10 -----> 1) 4p+6.5c = 47.5 ---> 2) multiply 1st equation by 4 4p + 4c = 40 ---> 3) subtract 3rd equation from the 2nd 2.5c = 7.5 c = 3 substituting c= 3 in 1st equation p+c = 10 p+3 = 10 p = 7 therefore 3 pounds of cashews and 7 pounds of peanuts are needed to make the mixture
