Nine, ten and one
Can you find the value of t in these equations?
Age
11 to 14
Challenge level
Problem
Suppose that e, i, n and t represent different positive whole numbers such that
n + i + n + e = 9
t + e + n = 10
and
i = 1
What is t?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
t = 5
We are given that 2n + e = 8 and t + e + n =10. Subtracting the first equation from the second gives t - n = 2.
As n cannot equal 1, the minimum value of t is 4 but this gives n = 2, e =4 which is not allowed.
If t = 5 then n = 3 and e = 2, which is allowed.
If t > 5 then n >3 and e is not a positive whole number, so 5 is the only possible value of t.
We are given that 2n + e = 8 and t + e + n =10. Subtracting the first equation from the second gives t - n = 2.
As n cannot equal 1, the minimum value of t is 4 but this gives n = 2, e =4 which is not allowed.
If t = 5 then n = 3 and e = 2, which is allowed.
If t > 5 then n >3 and e is not a positive whole number, so 5 is the only possible value of t.