No, unfortunately this isn’t a post about your favorite old-school Blink-182 song, but it's almost as exciting: We’re going to tackle age-related word problems. These questions present you with some clues about how old one or more people are, and then ask you to figure out someone’s exact age or who’s oldest or something like that. Let’s take a look at a couple of examples:
Johnny is currently 4 times as old as his brother, Sam. In two years, Johnny will only be 3 times as old as Sam. How old was Johnny a year ago?
(A) 15
(B) 18
(C) 16
(D) 13
(E) 17
Time to set up our system of equations. We have two variables (Johnny’s age and Sam’s age) and two equations. Let’s say x = Johnny’s current age and y = Sam’s current age. The first line of the question says that Johnny is 4 times as old as Sam. This can be written as:
x = 4y (Equation I)
The second fact is that in two years Johnny will be 3 times as old as Sam (in 2 years!). Let’s write this as:
(x + 2) = 3(y + 2)
Multiply out the right side and we get:
x + 2 = 3y + 6 (Equation II)
Now, we have our system of equations! If we substitute 4y for x (from Equation I) into Equation II, we have:
(4y) + 2 = 3y + 6
y = 4.
Therefore, Sam is currently 4 years old. This means that Johnny is currently 16. Be careful: The question asks how old Johnny was a year ago. Johnny was 15—our answer is (A).
Here’s another type of “age” word problem you're likely to see on the test:
The four children in the Vuiler family are Violet, Remington, Paulius, and Zara. Remington is one of the two younger children. Paulius is not the youngest child. Violet is not the oldest or the youngest child. Zara is younger than Remington. Who is the second oldest child?
(A) Violet
(B) Remington
(C) Paulius
(D) Zara
(E) Not enough information to tell
There's a lot of information to digest there. Let’s create a quick chart to organize all of the facts. We’ll write down each child and what “age rank” each could possibly be. From this, we can visually see our information and find our answer. We’ll put a “x” for possible option and a “y” for confirmed “age rank.”
| Youngest | 2nd youngest | 2nd oldest | Oldest | |
| Violet | ||||
| Remington | ||||
| Paulius | ||||
| Zara |
Remington is either the youngest or second youngest. Paulius is not the youngest—so he must be either the oldest, second oldest, or second youngest. Violet is neither the oldest or youngest—so she must be either the second oldest or second youngest. Zara is younger than Remington—let’s leave her off for now because we’re not quite sure where to put her.
| Youngest | 2nd youngest | 2nd oldest | Oldest | |
| Violet | x | x | ||
| Remington | x | x | ||
| Paulius | x | x | x | |
| Zara |
Remington is one of the youngest two: In order for Zara to be younger than Remington, Zara would have to be the youngest. This means that Remington is the second youngest: There’s no where else to put him.
| Youngest | 2nd youngest | 2nd oldest | Oldest | |
| Violet | x | x | ||
| Remington | y | |||
| Paulius | x | x | x | |
| Zara | y |
Paulius and Violet can’t be the second youngest now—they must be the two older children. Violet has no other option but to be the second oldest, and Paulius must be the oldest.
| Youngest | 2nd youngest | 2nd oldest | Oldest | |
| Violet | y | |||
| Remington | y | |||
| Paulius | y | |||
| Zara | y |
Use the facts to confirm your answer. Answer (A) is correct, since Violet is the second oldest child.
Let’s review a few key points for solving questions about age:
Get rocking with some age-finding in this quiz.
Got a math problem you can’t solve? Drop it in the comments or email it to testpreptutor@sparknotes.com.
Related Post: What The...What Is That Crazy Symbol?!?
By: Adam
Topics: SAT, act, math, word problems, age
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