If x pounds of cashews valued at $6.00 per pound are to be mixed with y pounds of peanuts valued at $4.00 per pound to obtain a 40 pound cashew-peanut mixture.

Question

Find x and y so that when the mix is sold for $4.75 per pound, the same amount of revenue
is collected from the sale of the mix as would have been collected from the sale of each type of nut individually. Set up an appropriate system of linear equations and solve it to determine x and y.

Answer 1

obvious first equation:
x + y = 40

2nd equation deals with value of the nuts

6x + 4y = 4.75(40)
6x + 4y = 190
3x + 2y = 95 **
double the first one: 2x + 2y = 80 ***

subtract *** from **
x = 15
in your head looking at x+y = 40
y = 25

check:
6(15) + 4(25) = 190
4.75(40) = 190