To begin we will create two equations. One to represent the age of the dog (in dog years), and one to represent the age of the cat (in cat years).
Dog: It is given that the current age of the dog in dog years is 16. For every human year the dog ages 7 dog years. If we let x represent the number of human years that have passed and y represents the age of the dog, we can write the following equation for the dog's age in dog years.
y=16+7x
Cat: It is given that the current age of the cat in cat years is 28. For every human year the cat ages 4 cat years. Since x represents the number of human years that have passed and y represents the age of the cat, we can write the following equation for the cat's age in cat years.
y=28+4x
To find the number of human years it will take for the animals to reach the same age in their respective years we must find the value of x that makes the equations equal the same y-value. We can determine this graphically.
From the graph we can see that the lines intersect at (4,44). This means that after 4 more human years both animals will be 44 years old in their respective years.
