The sum of two numbers is 25. One of the numbers exceeds the other by 9. Find the numbers.

Question

no additional details 

Answer 1

x and x+9 are the numbers

x+x+9=25

2x+9=25

2x=25-9

2x=16

x=16/2

x=8

x+9=8+9=17

8 and 17 are the numbers

 

if you are not in algebra, here is another solution:

25/2=12.5

12+13=25

11+14=25

10+15=25

9+16=25

8+17=25  answer

you can do this because 25 is a small number and trial and error, although not the best strategy, is a mathematical strategy that you can use

 

Answer 2

We start by writing out the statements algebraically.

The first sentence is the same as saying x+y=25.

The second sentence is saying x-y=9.

 

We now have a system of equations.

Writing the two equations on top of each other, we can use elimination or substitution to solve. These equations make for an easy elimination process, as we can eliminate y when we add the two equations.

 

x + y = 25

x -  y =   9

2x      = 34

 

Divide by 2 on both sides, and we get x = 17.

Substitute back in to either equation - I will use the latter equation...

 

17 - y = 9

Switch the places of y and 9 (subtract 9 from both sides, add y to both sides), and we get:

 

17 - 9 = y

This is a simple subtraction problem - giving us y = 8.

 

Check your answer using the other equation:

17 + 8 = 25 -> this answer is correct, so we know our answer works.