Question

A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets PhP1000 more than D, what is B's share?

Answer 1

Given :-

• A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3.

• C gets PhP1000 more than D

To Find :-

• Share of B.

Concept Used :-

Writing Systems of Linear Equation from Word Problems

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3 Carry out the plan and solve the problem.

Solution :-

Since,

A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3.

$\begin{gathered}\begin{gathered}\bf \: Let \: share \: of - \begin{cases} &\sf{A \: be \: 5x} \\ &\sf{B \: be \: 2x}\\ &\sf{C \: be \: 4x}\\ &\sf{D \: be \: 3x} \end{cases}\end{gathered}\end{gathered}$

According to statement,

C gets PhP 1000 more than D.

So,

Share of C - Share of D = 1000

$\sf \: 4x - 3x = 1000$

$\bf \: \therefore \: x \: = \: 1000$

So,

Share of B = 2x = 2 × 1000 = Php 2000.