January 2022
Problem of the Month

1876 M.I.T. Exam question

Mathematician Presh Talwalkar frequently digs up samples of classic college entrance exams so his followers can see how they'd fare in the days before standardized testing.

Recently, Talwalkar unearthed a question from an 1876 algebra exam given to applicants at the Massachusetts Institute of Technology.   Can you solve it?

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?"

Solution to the problem

The father is 50 years old and the son is 18 years old.

Let F = age of the father now.
Let S = age of the son now.

Then we can write two equations:
F - 2 = 3 (S - 2)
F + 14 = 2 (S + 14)

Distributing, we get:

F - 2 = 3S - 6
F + 14 = 2S + 28

From the first equation, F = 3S - 4 which we can substitute into the second equation: (3S - 4) + 14 = 2S + 28
S = 18.
Therefore, F = 3 (18) - 4 = 50.

Correctly solved by:

1. Dr. Hari Kishan	D.N. College, Meerut, Uttar Pradesh, India
2. Veena Mg	Bangalore, Karnataka, India
3. Ivy Joseph	Pune, Maharashtra, India
4. Colin (Yowie) Bowey	Beechworth, Victoria, Australia
5. Ryan Huff	Central High School, Grand Junction, Colorado
6. Mohamed Sheriff (MEDDORA)	Freetown, Western Area Urban District, Sierra Leone, West Africa
7. Brijesh Dave	Mumbai City, Maharashtra, India
8. Kelly Stubblefield	Mobile, Alabama
9. Alan Rench	Armstrong Creek, Wisconsin
10. Ritwik Chaudhuri	Shantiniketan, West Bengal, India

Send any comments or questions to: David Pleacher