Question

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.

Answer 1

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