Expert: Sherman D. - 5/23/2006

Question
I have this tought question and would need your help.The question sounds like this:

Mike has bought a numbers of x chicken with price at a each.
He also bought a numbers of y duck with price at b each.
All together he has spend $208. ax+by=208
Total numbers of chicken and duck is 20. x+y=20
b is bigger than a. b>a

Please find the value of x,y,a and b.

Answer
ax + by = 208
x + y = 20

x + y = 20
y = -x + 20

ax + b(-x + 20) = 208
ax - bx + 20b = 208
(a - b)x + 20b = 208

(a - b)x = -20b + 208
(a - b)x = -20(b - (52/5))
x = (-20(b - (52/5)))/(a - b)

y = -((-20(b - (52/5)))/(a - b))
y = (20(b - (52/5)))/(a - b)

ax - bx + 20b = 208
ax - b(x - 20) = 208
ax = b(x - 20) + 208
a = (b(x - 20) + 208)/x

ax - bx + 20b = 208
ax - b(x - 20) = 208
-b(x - 20) = -ax + 208
-b = (-ax + 208)/(x - 20)
b = (ax - 208)/(x - 20)

------------------------------------

a = (b(x - 20) + 208)/x
b = (ax - 208)/(x - 20)
x = (-20(b - (52/5)))/(a - b)
y = (20(b - (52/5)))/(a - b)

using that
x = 1-19
y = 19-1

Since this will take to long for me to do, i recommend going to answers.yahoo.com for further help.