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

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.

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.