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

Question

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

Answer 1

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.

Answer 2

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.