last month , he sold 50 chickens and 30 ducks for $550 . This month , he sold 44 chickens and 36 ducks for $532. How much does a chicken cost , and how much does a duck cost ?
Accepted Solution
A:
Hello there, my fellow human being! So, the chicken costs $8 and the duck costs $5, here's why.
Let's say x is the cost of a chicken while y is the cost of a duck. We can make two linear equations using the information above. Last month, he sold 50 chickens and 30 ducks for $550: 50x + 30y= 550 This month, he sold 44 chicken and 36 ducks for $532: 44x + 36y = 532
50x/10 + 30y/10 = 440/10 44x/4 + 36y/4 = 532/4
5x + 3y = 44 11x + 9y = 133
So, now that we have our answer simplified, we have to use elimination to solve this system of equations. But, first we need to make sure that at least one of our variables is able to be canceled out. Let's multiply this equation by -3. (5x + 3y = 44) * -3.