Question

divide a sum of rs 1110 between A,B and C so that for every rs 8 given to A,B may get Rs 5 and for every Rs 7 given to B ,C may get rs 4​

Answer 1

In this question, an amount is divided between three parts. From this, relations between the variables are used to find the amount corresponding to each part.

Sum of 1110 between A, B and C:

This means that:

$A + B + C = 1110$

For every rs 8 given to A,B may get Rs 5

This means that:

$\frac{A}{B} = \frac{8}{5}$

And thus:

$5A = 8B$

$A = \frac{8B}{5}$

For every Rs 7 given to B ,C may get rs 4​

This means that:

$\frac{B}{C} = \frac{7}{4}$

And thus:

$7C = 4B$

$C = \frac{4B}{7}$

Amount of B:

Replacing into the original equation:

$A + B + C = 1110$

$\frac{8B}{5} + B + \frac{4B}{7} = 1110$

$\frac{56B + 35B + 20B}{35} = 1110$

$111B = 1110*35$

$B = \frac{1110*35}{111}$

$B = 350$

Amounts of A and C:

A and C are given as functions of B, so:

$A = \frac{8B}{5} = \frac{8*350}{5} = 560$

$C = \frac{4B}{7} = \frac{4*350}{7} = 200$

Thus:

The amount given to A is of Rs 560, to B is of Rs 350 and to C is of Rs 200.

For another problem involving divisions given ratios, you can check https://brainly.com/question/23857756.

Answer 2

A, B and C receive RS. 560, RS. 350 and RS. 200, respectively.

In this problem, we must translate the sentences into mathematical expression. Please notice that systems of linear equations are resoluble if the number of formulas equals the number of variables. In other words, we must have three linear equations for three variables:

1) Divide a sum of RS 1110 between A, B, C:

$a + b + c = 1110$ (1) Var: 3, Eqs: 1  

2) So that for every RS 8 give to A, B may get RS 5:

$\frac{a}{b} = \frac{8}{5}$

$5\cdot a - 8\cdot b = 0$ (2) Var: 3, Eqs: 2

3) And for every RS 7 given to B, C may get RS 4:

$\frac{b}{c} = \frac{7}{4}$

$4\cdot b -7\cdot c = 0$ (3) Var: 3, Eqs: 3

Now we solve the resulting system, the solution set of the system is:

$a= 560$, $b = 350$, $c = 200$

A, B and C receive RS. 560, RS. 350 and RS. 200, respectively.