Collin is 69 years old. Erica is 33 years old. How many years ago was Collin's age 5 times Erica's age?

Answer 1

We can express Collin's age (we will use the variable "C" for this) as a function of how many years ago it was (we will use the variable "y" for this) as:

C = 69 - y (Equation 1)

Similarly, we can express Erica's age (using the variable "E") as:

E = 33 - y (Equation 2)

If we set Collin's age equal to 5 times Erica's age, that gives us the following equation:

C = 5*E (Equation 3)

We can write this in terms of "y" by using Equations 1 and 2.

(69 - y) = 5*(33 - y)

Distributing the 5 on the right hand side yields:

69 - y = 5*33 - 5*y

69 - y = 165 - 5*y

To isolate "y", we first subtract both sides by 69:

69 - y - 69 = 165 - 5*y - 69

-y = 96 - 5*y

We then add 5*y to both sides:

-y + 5*y = 96 - 5*y + 5*y

4*y = 96

Lastly, we divide both sides by 4:

4*y/4 = 96/4

y = 24

Thus, the answer is 24 years ago. We can check this by seeing that Collin was 45 (69-24) years old and Erica was 9 (33-24), which times 5 equals 45.