Ratios

[KWF]

Suppose that an amount of money ($1,200) is to be divided or shared in the following:

$1,200 shared in a ratio of 1/2 to 3/4 or the same amount shared in a ratio of 40% to 70%.

Are these examples incorrect? If so, why?
When these amounts are added, the sums are more than 1.
1/2 + 3/4 = 5/4 or 1 1/4 and 40% +70% = 110%.

 

[Ishuda]

Suppose that an amount of money ($1,200) is to be divided or shared in the following:

$1,200 shared in a ratio of 1/2 to 3/4 or the same amount shared in a ratio of 40% to 70%.

Are these examples incorrect? If so, why?
When these amounts are added, the sums are more than 1.
1/2 + 3/4 = 5/4 or 1 1/4 and 40% +70% = 110%.

The amount isn't 1/2 and 3/4, the ratio of the amount share is 1/2 to 3/4.

As an example suppose you had a given amount of D dollars and Able received a dollars and Bob received b dollars. Then
a+b=D
Also suppose that the ratio of what Able received to what Bob received is a ratio of 27/4 to 9/4. Then
a/b = (27/4) / (9/4).

You now have two linear equations in two unknowns. Generally there is a unique solution for the two unknowns a and b. Suppose D were $2800
a/b = (27/4) / (9/4) => a = b * (27/4) * (4/9) = 3 b
Thus
a+b = 3 b + b = 4b = 2800
So b = $700 and a=$2100

 

[Deleted member 4993]

Suppose that an amount of money ($1,200) is to be divided or shared in the following:

$1,200 shared in a ratio of 1/2 to 3/4 or the same amount shared in a ratio of 40% to 70%.

Are these examples incorrect? If so, why?
When these amounts are added, the sums are more than 1.
1/2 + 3/4 = 5/4 or 1 1/4 and 40% +70% = 110%.

As I see it:

ratio of 1/2 to 3/4 = 2/3 = 0.667

ratio of 40%/70% = 0.4/0.7 = 0.571

NOT equal....