Word problem using elimination

Question

The sum of the digits of a three-digit number is 16. The units digit is 2 more than the sum of

the other two digits and the tens digit is 5 more than the hundreds digit. What is the number?

Answer 1

Using elimination is a good way to prepare for matrix operations (to learn later).

Let the number be "abc" with digits a, b, and c.

a + b + c = 16 "sum of the digits ... is 16"

-a -b + c = 2 "units digit is 2 more than the sum of other two digits" c = 2 + a + b

-a + b = 5 "tens digit is 5 more than the hundreds digit" b = a + 5

For elimination, look for opposite signs (to subtract equations) or for same signs (to add equations).

Add the first two equations to get 2c = 18 Thus, c=9

Now, add the first and the third equation to get 2b + c = 21

then subtract c = 9

to get 2b = 12 Thus, b = 6

Now, use the third equation:

-a + b = 5

b = 6

-a = -1 (subtracted equations) so, a=1

Be sure to check your answers:

1 + 6 + 9 = 16 YES

-1 -6 + 9 = 2 YES

-1 + 6 = 5 YES

The number is 169.