Thanks for your word-problem question, Kaye. This is a system of linear equations problem, which we'll solve using the Substitution Method. (Learn more about the Systems of Linear Equations Substitution Method.) Let's review the facts first:

• Jerry's age today is J
• Grandpa's age today is G
• Jerry's age 15 years ago is (J-15)
• Grandpa's age 15 years ago is (G-15)

In equation form, then, we can express their ages 15 years ago and today like so:

• #1: J - 15 = (G-15)/3 (age 15 years ago)
• #2: J + G = 110 (age today)

Solve equation #2 for grandpa's age by subtracting J from both sides, yielding:

#2: G = 110 - J

Now substitute this definition of G into equation #1 so we can solve for J:

#1: J-15 = ((110-J)-15)/3, or
#1: J-15 = (95-J)/3, or
#1: 3(J-15) = (95-J), or
#1: 3J-45 = 95-J, or
#1: 3J = 95-J+45, or
#1: 3J+J = 95+45, or
#1: 4J = 140, or
#1: J = 35

So if J=35, then that means Jerry's age today is 35 years old. Using equation #2, that means Grandpa's age today is 110-35, or 75 years old.

The final step in solving this problem is one that many students forget: checking your answer! Let's put our values for J and G into equations #1 and #2 and make sure they work:

#1: 35-15 = (75-15)/3, or
#1: 20 = (60)/3, or
#1: 20 = 20 CORRECT

#2: 75 = 110-35, or
#2: 75 = 75 CORRECT

The correct answer, then, is that Jerry's grandfather is 75 years old.

KG, thank you for this algebra question.

The easiest way to solve this system of equations problem is by using the graphing method.

(Use the illustration to the left for a helpful guide.) If we graph the first equation, we get a diagonal line passing through the origin sloping upwards. (See the blue line in the illustration.) Graphing the second equation gives us a diagonal passing through the origin and sloping downwards. (See the pink line in the illustration.)

From visual inspection, we can see that the lines intersect at one place only -- the origin. Thus, the solution to this system is (0,0).