   SEARCH HOME Math Central Quandaries & Queries  Question from Tiffany, a student: The sum of two number is 29.The difference is 1. What are the two numbers? We have three responses for you

Tiffany,

Say this is a leap year in February, so there are 29 days in this month. On each day of the month, I decide whether or not I will wear a tie that day.

If after the month is done I wore my tie 1 more day than the number of days I didn't wear my tie, how many days did I wear it?

Do you know some algebra, Tiffany?

If we let T = the number of days I didn't wear my tie, then T + 1 is the number of days I wore it. Added together, that is 29 days.

So T + (T + 1) = 29. Find the value of T.

Hope this helps,
Stephen La Rocque.

Tiffany,

You can also solve this using "guess and check".

The two numbers are very close together, they only differ by 1. As a place to start the "guess and check" consider the problem

The sum of two number is 29.The difference is 0. What are the two numbers?

Penny

Hey Tiffany,
In order to solve this problem you need to translate the words into mathematical statements.
When a statement says 'a number' we can represent this number with a variable (like 'x' or 'y').
Words like sum and difference are operations in math like add (+) or subtract (-).
And the statement 'is' or 'becomes' represents equals.
Your particular question needs 2 equations (because of the two 'is'). Take a look at this question,

The sum of two numbers is 31 and their difference is 9.
+ = - =
Let x = one number, Let y = other number
x + y = 31, x - y = 9
We now have two equations:
(1) x+y=31
(2) x-y=9
We have to choose one to isolate a variable (a letter),
(2) x-y=9 work on both sides,
x-y +y=9+y
x+0=9+y
x=9+y Now substitute this in the other equation,
(1) x+y=31
(9+y)+y=31 and solve for y,
9 + 2y=31
9-9+2y=31-9
2y=22
2y/2=22/2
y=11 we can sub this into either equation to solve for x,
(2) x-y=9
x-11=9
x-11+11=9+11
x=20
We can check our answers using the original equations:
(1) x+y=31
20+11=?31
31=31 (it checks!)
(2) x-y=9
20-11=?9
9=9 (it checks!)
If we look back to our original equation, one number (x) is 20 and the other number (y) is 11.
Hope this helps.
Melanie     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.