Question

At a livestock market, one customer purchased 4 sheep and 2 cows for a total of $1660. Another customer purchased 3 sheep and 5 cows for a total of $2925. Create a system of equations and solve it with substitution or elimination, and find the price of a sheep, and the price of a cow.

Answer 1

`s \approx \$182.14`

`c \approx \$435.72`

Explanation:

Set up a system of equations, where s is the cost of a sheep and c is the cost of a cow:

`4s + 2c = \$ 1660`,
`3s + 5c = \$ 2925`

First, isolate c in the first equation.

`4s + 2c = \$ 1660`

`2c = \$ 1660 - 4s`

`c = \$ 840 - 2s`

Next, substitute this value into the second equation:

`3s + 5c = \$2925`

`3s + 5(\$840 - 2s) = \$2925`

and simplify.

`3s + \$4200 - 10s = \$2925`

`-7s = -\$1275`

`7s = \$1275`

`s \approx \$182.14`

Finally, plug this value into the first equation to get the value of c:

`4(\$182.14) + 2c = \$1660`

`2c = \$1600 - \$728.57`

`c \approx \$435.72`

So, a sheep costs about $184.14, and a cow costs about $435.72.