Question

Is this correct so far?

The Nut Barn requires 15 pounds of mixed walnuts and pecans from their wholesaler. Walnuts cost $2.26 per pound and pecans cost $1.96 per pound. How many pounds of pecans are needed if they only want to pay $2.18 per pound for the mixture?

Answer 1

p = pecans
w = walnuts

Two Equations:

w + p = 15
2.26w + 1.96p = 2.18(w + p)


Solve for w in first equation.

w + p = 15
subtract
-----------
w = p - 15

Plug in this new information into second equation.

2.26(p - 15) + 1.96p = 2.18((p - 15) + p)
distribute
-----------------------------------------
2.26p - 33.9 + 1.96p = 2.18((p - 15) + p)
subtract
-----------------------------------------
2.26p + 1.96p = 2.18((p - 15) + p) + 33.9

Answer 2

it looks ok, but I would replace (w+p) in the 2nd equation with 15 immediately (you know w+p=15)

Answer 3

2.26(p - 15) + 1.96p = 2.18(15)
multiply
-------------------------------
2.26(p - 15) + 1.96p = 37.2
distribute
-------------------------------
2.26p - 33.9 + 1.96p = 37.2
subtract
-------------------------------
2.26p + 1.96p = -71.1
add
-------------------------------
4.22p = -71.1
divide
-------------------------------
p = 16.84834123

Answer 4

I did that and solved, but got a bunch of decimal points... What's wrong?

Answer 5

how did you get -71.1?

Answer 6

I subtracted -33.9 on both sides

Answer 7

I think you should add +33.9 to both sides
that way the -33.9 + 33.9 on the left will add to zero.

Answer 8

ahhhh Right. Okay I'll do that now. :)

Answer 9

no, wait... first
fix
w+p= 15
add -p to both sides
w+p-p= 15-p

or w= 15-p

you are using w= p-15 which is not good.

Answer 10

Got it. P = 11. :) Thanks!