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4.A pet store sells cats for $50 and dogs for $100. If one day it sells a total of 4pets and makes $300, find out how many cats and dogs it sold by writing asystem of equations and graphing to solve it.Representations:Equations:

Sagot :

Answer:

2 cats and 2 dogs

Explanation:

Representations:

x = number of cats sold

y = number of dogs sold

Equations:

We know that it sells a total of 4 pets, so the sum of the number of cats and dogs is 4. So:

x + y = 4

On the other hand, they make $300, and they make $50 for each cat and $100 for each dog, so:

$50x + $100y = $300

So, the system of equation is:

x + y = 4

50x + 100y = 300

Graph:

Now, we need to graph the equations, so we need to identify two points for each equation:

For x + y = 4

If x = 0, then:

0 + y = 4

y = 4

If x = 4, then:

4 + y = 4

4 + y - 4 = 4 - 4

y = 0

For 50x + 100y = 300

If x = 0, then:

50(0) + 100y = 300

100y = 300

100y/100 = 300/100

y = 3

If x = 4, then:

50(4) + 100y = 300

200 + 100y = 300

200 + 100y - 200 = 300 - 200

100y = 100

100y/100 = 100/100

y = 1

Therefore, we have the points (0, 4) and (4, 0) to graph the line of the first equation and the points (0, 3) and (4, 1) to graph the line of the second equation.

So, the graph of the system is:

Therefore, the solution is the intersection point (2, 2), so they sold 2 cats and 2 dogs that day.

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