Question

The difference between two positive numbers is 48 , The lesser number is 1/3 if the greater number . What are the two positive numbers? A- 6 and 54. B-12 and 60 C-30 and 78 D - 24 and 72

Answer 1

So, the correct answer is option D: The two positive numbers are x=72 and y=24.

Explanation:

Let's denote the greater number as x and the lesser number as y. The problem gives us two pieces of information:

1. The difference between two positive numbers is 48: x−y=48.
2. The lesser number is
   `(1)/(3)` of the greater number:
   `y= (1)/(3) x`

Now, let's solve this system of equations:

From the second piece of information, we can express y in terms of
`x: y =(1)/(3) x`

Substitute this expression for y into the first equation:

`x-((1)/(3) x)=48`

Combine the terms on the left side:

`(2)/(3) x=48\\`

Now, solve for x:

`x = (48(3))/(2)`

x = 72

Now that we know x, we can find y using the second piece of information:

`y= (1)/(3) *72\\y= 24`

So, the correct answer is option D: The two positive numbers are x=72 and y=24.