algebra problem-mixtures?

Question

the question is:

A grocer mixes pecans priced at $4.50 per pound with almonds priced at $5.25 per pound. How many pounds of each type of nut should he use to have a total mixture of 14 pounds priced at $4.80 per pound?


i set up the equations as:
x=pecans, y=almonds
x+y=14
and
4.50x+5.25y=4.80

i tried substituting and graphing but i can't get the right answer...

Answer 1

well almost there -

the last needs adjusting (forgot to add the weight)
4.5x + 5.25y = 4.8 x 14
4.5x + 5.25y = 67.2
4.5x + 5.25(14-x) = 67.2
4.5x + 73.5 - 5.25 x = 67.2
73.5 - .75x = 67.2 ....add .75x to both sides
73.5 = 67.2 + .75x....subtract 67.2 from both sides
6.3 = .75 x....divide both sides by .75
x = 8.4 = pecans
14 - 8.4 = 5.6 almonds

tada

Answer 2

x+y=14

4.50x+5.25y=80

change the first one to slope-intercept form
y= -x+14

plug it in the second

4.50x + 5.25(-x+14)=80

distribute the 5.25
4.50x - 5.25x + 73.5 = 80

move the 73.5 over by subtracting

4.50x - 5.25x = 6.5

combine like terms

-0.75x = 6.5

divide both sides by -0.75

x= -8.67