Question

A farmer sells cows for $350 each and chickens for $75 apiece. At market, he sold 11 animals for a total of $2475. How many of each animal were sold?

Answer 1

Let's use algebra to solve this problem.

Let's start by defining some variables to represent the number of cows and chickens the farmer sold. Let c be the number of cows and h be the number of chickens. We know that the farmer sold a total of 11 animals, so:

c + h = 11 (Equation 1)

We also know that the total amount of money the farmer received was $2475. The amount he received from selling cows was $350 times the number of cows, or 350c. The amount he received from selling chickens was $75 times the number of chickens, or 75h. So:

350c + 75h = 2475 (Equation 2)

Now we have two equations with two unknowns. We can solve for one variable in terms of the other in the first equation:

c + h = 11

c = 11 - h

We can substitute this expression for c into the second equation:

350c + 75h = 2475

350(11 - h) + 75h = 2475

Simplifying and solving for h:

3850 - 350h + 75h = 2475

-275h = -1375

h = 5

So the farmer sold 5 chickens. We can substitute this value of h back into the first equation to find c:

c + h = 11

c + 5 = 11

c = 6

Therefore, the farmer sold 6 cows and 5 chickens.