2002 CEMC Gauss (Grade 8) Problems/Problem 6

The following problem is from both the 2002 CEMC Gauss (Grade 8) #6 and 2002 CEMC Gauss (Grade 7) #12, so both problems redirect to this page.

Problem

Qaddama is years older than Jack. Jack is years younger than Doug. If Qaddama is years old, how old is Doug?

Solution 1

Since Qaddama is years older than Jack, Jack's age must be less than Qaddama's age. Thus, Jack's age is .

Since Jack is years younger than Doug, Doug's age must be more than Jack's age. Thus, Doug's age is .

~anabel.disher

Solution 2 (using a variable)

Let be Qaddama's age.

Since Qaddama is years older than Jack, Jack's age is .

Since Jack is years younger than Doug, Doug's age is .

We can now plug-in because we know that's Qaddama's age from the third sentence of the problem. We then see that Doug's age is .

~anabel.disher