plz help me!

Question

Find four numbers proportional to the numbers 2, 4, 5, and 6 if the difference between the sum of the two last numbers and the sum of the first two numbers is equal to 4.8.

Answer 1

Hi Areniy!

 

If the four numbers are proportional to the numbers 2, 4, 5, and 6, then we can say the four numbers are 2n, 4n, 5n, and 6n for some value of n.

 

Now, let's interpret what "the difference between the sum of the two last numbers and the sum of the first two numbers is equal to 4.8 really means:

 

The sum of the last two numbers is 5n + 6n = 11n

The sum of the first two numbers is 2n + 4n = 6n

 

The difference between these is 11n - 6n = 5n

and that value is equal to 4.8

 

So 5n = 4.8

which, after we divide by 5, makes the value of n = .96

 

This makes the numbers 2n, 4n, 5n and 6n equal to 

2(.96) = 1.92

4(.96) = 3.84

5(.96) = 4.8

6(.96) = 5.76

 

A quick check will verify that the two largest numbers minus the two smallest numbers is

 

(5.76 + 4.8) - (1.92 + 3.84)

6.24 - 5.76

4.8   as we expected!

 

Hope this helps!