Understanding Ratios

[KWF]

If two people share $600.00 in a ratio of 2 to 3, which calculation is correct

2/3 X $600.00 or 2/5 X $600.00? The denominator 5 is determined by adding 2 and 3 from the ratio.

 

[Ishuda]

If two people share $600.00 in a ratio of 2 to 3, which calculation is correct

2/3 X $600.00 or 2/5 X $600.00? The denominator 5 is determined by adding 2 and 3 from the ratio.

The long way around:

Suppose you have two people get A and B amounts of a total amount D in a ratio of a to b. Then
A / B = a / b
or
A = (a / b) B
We also have
A + B = D
so
(a / b ) B + B = D
and
(a + b) B = b D
or
B = \(\displaystyle \frac{b}{a + b}\) D
and, since B = (b / a) A
A = \(\displaystyle \frac{a}{a + b}\) D

So it looks like the denominator is gotten by adding the two parts.

 

[KWF]

2 p + 3 p = 600
5 p = 600
p = 600/5 = 120 : so 240 and 360

This is the same as the following:

2/5 X $600 = $240 + 3/5 X $600 = $360. So, 2/5 is used and not 2/3.

Thanks for the different calculation!