The sum of two numbers is 70. One number is 8 more than the other. What's the smaller number?

• A. 31
• B. 33
• C. 35
• D. 36

Answer: (A)

To find the smaller number, we can set up two equations based on the information given.

Let the smaller number be represented by ( x ). Since one number is 8 more than the other, the larger number can be expressed as ( x + 8 ). According to the problem, the sum of the two numbers equals 70. Therefore, we can write the equation:

[ x + (x + 8) = 70 ]

Combining like terms results in:

[ 2x + 8 = 70 ]

Next, we can solve for ( x ) by first subtracting 8 from both sides:

[ 2x = 70 - 8 ]

[ 2x = 62 ]

Now, dividing both sides by 2 gives us:

[ x = 31 ]

This calculation shows that the smaller number is indeed 31. To verify, we can check the larger number, which is ( 31 + 8 = 39 ). Adding both numbers together:

[ 31 + 39 = 70 ]

This confirms that the calculations are correct. Thus, the smaller number is 31.