Know total amount. Must divide in two parts so that one part is 10% from another part.

I know total amount.

Must divide the total amount in two parts. Smaller part (amount) is 10% of bigger part (amount) so that smaller part plus bigger part is total amount.

So total is 17091.54

Bigger part is 15537.76

Calculate 10% from 15537.76 and get smaller part 1553.78

15537.76 + 1553.78 = 17091.54

But what is the formula to get either 15537.76 (90%) or 1553.78 (10%) knowing only total 17091.54 (100%)?

If 17091.54 * 0.9 = get 15382.39 (not correct)

As know formula is something like (17091.54 - 15382.39) / ((1-0.9)+0.9). But result is not correct (1709.15)

Update

I can only get result following long way.

17091.54 = 100

17091.54 / 100 = 0.005850849

To get proportion of 15537.76 to 17091.54, divide 15537.76 by 0.005850849 = 90.90909091

Then 100 / 90.90909091 = 1.1

Then 17091.54 / 1.1 = 15537.76

But this seems not the best way.

Please advice what would be better way

In the Singapore education system, children are encouraged to solve this sort of problem with model drawing. Previously, I would've immediately resorted to algebra like Claude, but after having taught my 9-year old, I now draw models! :)

It's quite simple. 10% is one-tenth. So represent the small part as 1 unit. The large part is therefore 10 units. The total is 11 units, and that's 17091.54

So 1 unit = 17091.54/11 = 1553.776363636...

Therefore the small unit is 1553.78 and the large unit is 10*1553.7763 = 155377.76

I'm rounding off both answers to 2 decimal places like the total figure. They won't add up to exactly the total because of round-off errors but it'll be close.

I just wanted to illustrate a more "elementary" method than algebra to do this.

Hint

Let us call $S$ the smaller part, $B$ the bigger part and $T$ the total amount.

WHat you are told is that $S=\frac{B}{10}$ and that $S+B=T$. So, you have now two linear equations for the two unknowns $S$ and $B$ since $T$ is given.

I am sure that you can take from here.