Shares Ratio Calculation Method

Let the shares of A, B, and C be represented by $A$, $B$, and $C$ respectively.

We are given the following information:

• The total amount is 49: $A + B + C = 49$.
• A receives 5 more than B: $A = B + 5$.
• B receives 4 more than C: $B = C + 4$.

Expressing Shares in Terms of One Variable

We can express the shares of A and B in terms of C:

• Since $B = C + 4$.
• Substitute this into the equation for A: $A = (C + 4) + 5 = C + 9$.

Now, all shares are defined relative to C.

Calculating Individual Shares

Substitute the expressions for A and B into the total amount equation:

$(C + 9) + (C + 4) + C = 49$

Combine the terms:

$3C + 13 = 49$

Solve for C:

$3C = 49 - 13$

$3C = 36$

$C = \frac{36}{3}$

$C = 12$

Now find B and A:

• $B = C + 4 = 12 + 4 = 16$.
• $A = B + 5 = 16 + 5 = 21$.

Determining the Ratio

The shares are $A=21$, $B=16$, and $C=12$.

The ratio of their shares $A:B:C$ is $21:16:12$.