Question

Find two numbers such that one number is 1/2 more than 1/4 the other number, and the sum of the numbers is eight. What is the value of the smaller number?

Answer 1

The two numbers where one is half more than one-fourth of the other and their sum is eight are 6 and 2, with 2 being the smaller number.

Step-by-step explanation:

To find two numbers where one number is half more than one-fourth of the other number, and their sum is eight, we can set up two equations. Let's call the larger number x, and the smaller number y. The problem tells us:

1. y = (1/4)x + 1/2
2. x + y = 8

Substituting the first equation into the second equation gives:

1. x + (1/4)x + 1/2 = 8
2. 5/4x + 1/2 = 8
3. 5/4x = 8 - 1/2
4. 5/4x = 15/2
5. x = (15/2) / (5/4)
6. x = 6

Now that we have the value of x, we can find y:

1. y = (1/4)(6) + 1/2
2. y = 3/2 + 1/2
3. y = 2

So the larger number is 6 and the smaller number is 2.