Question

Michael breeds chicken and ducks

last month he sold 50 chickens and 30 ducks for $550. this month he sold 44 chicken's and 36 ducks for $532.
how much Does a chicken cost and how much does a duck cost?​

Answer 1

cost of a chicken $7.25

cost of a duck $4.25

Explanation:

Let c represent chickens and d represent ducks

50 chicken + 3 ducks = $550 ➡ 50c + 30d = $550

44 chicken + 36 ducks = $532 ➡ 44c + 36d = $532

Now find the difference of equations

(50c + 30d) - (44c + 36d) = $550 - $532

6c - 6d = $18

6×(c-d) = $18 divide both sides by 6

c - d = $3 Now we can use this information to find the cost of a chicken and duck

50c + 30d = $550

c - d = $3 multiply second equation by 30

30 × (c-d) = $3 ➡30c - 30d = $30

Now add this new equation we found to the very first equation

30c - 30d + 50c + 30d = $550 + $30 (-30d will eliminate 30d)

80c = $580 divide both sides of the equation by 80

c = $7.25

We know that c - d = 3 so now replace c by $7.25 the price we just found

$7.25 - d = $3

$7.25 - $3 = d

$4.25 = d