The Sister's Saving, Part I

Some steps were similar then I did in different way but got the same answer.

Here, is how I did it,

The names are quite confusing. So,

Let the savings of three sisters Sylvia's, Sylvanna's, and Sylvatra's saving be a, b, c.

Now,

a : b = 5 : 3 &

c : b = 6 : 5

b = 5 and 3

So, to make it equal we take the L.C.M. which is 15

We multiply the first and second ratio with 5 and 3 respectively.

a : b = 25 : 15 &

c : b = 18 : 15

So,

a = 25

b = 15

c = 18

It is said that the sum of their savings equal to 812

Let one part of their saving be x.

Then,

ax + bx +cx = 812

or 25x + 15x +18x = 812

or 58x = 812

or x = 812 / 58

x = 14

Now ,

a ------------------------------25x -------------------------------- 25 * 14 ----------------------------350

b ------------------------------15x -------------------------------- 15 * 14 ----------------------------210

c ------------------------------18x -------------------------------- 18 * 14 ----------------------------252

40 % of a = 40 / 100 * 350 = 140

So, c earns 140 + 252 = 392

Finally our answer is 392

Let x, y, and z be the value of Sylvia's, Sylvanna's, and Sylvatra's saving. It has been stated that $x : y = 5 : 3$ , and $z : y = 6 : 5$ . If we multiply the first ratio by $5$ , and the second ratio by $3$ , you will get this ratio:

$x : y : z = 25 : 15 : 18, x' = 25, y' = 15, z' = 18$

The money is Sylvia's account is:

$\frac {x'}{x'+y'+z'} \times (x+y+z)$

= $\frac {25}{25+15+18} \times 812$

= $\frac {25}{58} \times 812$

= $350$

The money is Sylvatra's account is:

$\frac {z'}{x'+y'+z'} \times (x+y+z)$

= $\frac {18}{25+15+18} \times 812$

= $\frac {18}{58} \times 812$

= $252$

$40$ % of Sylvia's saving is $\$140$ , so that the number of money in Sylvatra's account is: $252 + 140 = \boxed {392}$

P.S. The number of money in Sylvia's account is $350 - 140 = 210$ , while the number of money in Sylvanna's account is $812 - 350 - 252 = 210$ . This might help you to solve the next problem here :)