Question

A total of 34 dogs and cats participated in the pet store’s adoption event. The number of dogs that were adopted was 7 more than twice the number of cats. If a system of equations is written and graphed for this scenario, what does the point of intersection represent? Explain.

Answer 1

Sample Response: The intersection point represents the only solution of the scenario, which is how many dogs and how many cats participated in the pet store’s adoption event. One coordinate will represent the number of dogs, and the other coordinate will be the number of cats.

Answer 2

Let y represents the dog and x represents the Cat.

As per the Statement:

A total of 34 dogs and cats participated in the pet store’s adoption event.

⇒ x+y = 34 ......[1]

It is also given that the number of dogs that were adopted was 7 more than twice the number of cats.

"Twice times the number of cats" means 2x

"7 more than twice the number of cats means 2x + 7

⇒
`y = 2x + 7`

Then, system of equations are;

x +y = 34

y = 2x + 7

Now, plot the graph of these equation as show below:

The point intersection is, (9, 25) which represents 9 cats and 25 dogs are participated in the pet store's adoption event.