MIT Applicants Had to Solve This Viral Math Puzzle on the 1876 Entrance Exam

Mike Darling
·1 min read

From House Beautiful

On his popular YouTube channel, MindYourDecisions, mathematician Presh Talwalkar frequently digs up samples of classic college entrance exams.

Talwalkar challenges his followers to see how they’d fare in the days before standardized testing.

In one of his most recent videos, Talwalkar unearthed a question from an 1876 algebra exam given to applicants at the Massachusetts Institute of Technology.

It’s a simple prompt:

A father said to his son, “Two years ago I was three times as old as you; but in fourteen years I shall be only twice as old as you. What were the ages of each?”

As Talwalker goes on to explain, the solution is a relatively simple one, represented by the equation f-2 = 3 (s-2), if “f” and “s” represent the father and son’s ages, respectively.

Photo credit: Presh Talwalkar/Mind Your Decisions/YouTube
Photo credit: Presh Talwalkar/Mind Your Decisions/YouTube

Now for the second part: If the father will only be twice as old as his son in 14 years, their ages at that time can be represented by the equation f+14 = 2(s+14), with “f” and “s” once again standing in for the father and son.

“We now have a system of two equations and two variables,” Talwalkar says.

Photo credit: Presh Talwalkar/Mind Your Decisions/YouTube
Photo credit: Presh Talwalkar/Mind Your Decisions/YouTube

After some simple distribution, which you can watch above, Talwalker subtracts the second equation from the first, revealing the son’s age as 18 and the father’s age as 50.

If you’re up for another challenge, see if you have what it takes to solve this viral Amazon "hanging cable" problem.

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