Together these two turkeys weigh twenty pounds," said the butcher. The little fellow sells for two cents a pound more the big one." Mrs. Smith bought the little one for 82 cents and Mrs. Brown paid $2.96 cents for the big turkey. How much did each turkey weigh?

Question

I need the work also

Answer 1

Let the little fellow weigh x lbs
then the big fellow weighs 20-x lbs

let the cost of the big fellow be c cents per pound
then the cost of the little fellow is c+2 cents

x(c+2) = 82
cx + 2x = 82 #1

c(20-x) = 296
20c - cx = 296 #2

add #1 and #2
2x + 20c = 378
x + 10c = 189
x = 189-10c #3

I will let you finish it,
sub #3 into #1 to find c
then back into #3 to find x

cheap turkeys, must be old question

Answer 2

I don't get the last part:

I will let you finish it,
sub #3 into #1 to find c
then back into #3 to find x

Please help me through this!

Is it

(cx+2x) - (189-10c)?

Answer 3

x = 189-10c
then in #1
c(189-10c) + 2(189-10c) = 82
expanding this and lining it up as a quadratic
10c^2 - 169c - 296 = 0
I used the quadratic formula to get
c = 18.5

now back into #3
x = 189 - 10(18.5)
x = 4

so the little fellow weighed 4 lbs
and the big one weighed 16 lbs

the big one cost 18.5 cents a pound
the little one cost 20.5 cents a pound

check: 20.5x4 = 82
16x18.5 = 296