what are the two numbers?

Question

The sum of the two numbers are 69,and their difference is 7. What are the two numbers?

Answer 1

x+y=69

x-y=7

add

2x=76

x=76/2

x=38

38-y=7

38-7=y

y=31

38 and 31 are the numbers

Because the numbers are small you can use this arithmetic solution...

What 2 consecutive numbers add up to 69 ?

34 and 35, but their difference is 1

33 and 36, difference of 3

32 and 37, difference of 5

31 and 38, difference of 7 (the answer)

 

 

 

Answer 2

Let the first number be "x" and the second number be "y." Based on the first clue, we know that the first number plus the second number equals 69. So, we can restate this as x+y=69. Based on the second clue, we know that if we subtract one number from the other it equals 7. So, we can restate this as x-y=7 (or y-x=7, it doesn't matter). We want to be able to combine the two parts, so we must first solve for x. When we solve x+y=69 for x, we get x=69-y. Now, we plus this in for "x" in the second part, x-y=7. Since we just said x=69-y, that means 69-y-y=7, or 69-2y=7. Taking 69 to the other side, we get -2y=-62, or 2y=62. Dividing by 2, we get y=31. Now that we have y, all we have to do is plug that in to one of the original equations to find x. If we plus it into the first one, x+y=69, we get x+31=69. Subtracting 31, we get x=38. So, y=31 and x=38. These are your two numbers. If you double check, you will see that their sum is 69 and their difference is 7.

Answer 3

You can solve this by setting up the following equation:
the first number = x
since you know that the sum of the two numbers is 69, the second number = 69-x
you also know that the difference between the two number is 7, so your equation can be expressed as
 
x - (69 - x) = 7

 

Solve this equation as follows:

x - 69 + x = 7

2x - 69 = 7

2x = 7 + 69

2x = 76

x = 76/2 = 38

 

The second number is 69-x, or 69-38, which equals 31.

 

The two numbers are 38 and 31.