works.Example 11 The ratio of incomes of two persons is 9: 7 and the r

1.	works.Example 11 The ratio of incomes of two persons is 9: 7 and the ratio of theitexpenditures is 4 : 3. If each of them manages to save 2000 per month, find theirmonthly incomes.
Answer» Denote the incomes of the two person by 9x and 7x and their expenditures by 4y and 3y respectively. Then the equations formed in the situation is given by: 9x – 4y = 2000 ... (1) 7x – 3y = 2000 ... (2) Step 1: Multiply Equation (1) by 3 and Equation (2) by 4 to make the coefficients ofy equal. Then you get the equations: 27x – 12y = 6000 ... (3) 28x – 12y = 8000 ... (4) Step 2: Subtract Equation (3) from Equation (4) to eliminate y, because the coefficients of y are the same. So,you get (28x – 27x) – (12y – 12y) = 8000 – 6000 x = 2000 Step 3: Substituting this value of x in (1), 9(2000) – 4y = 2000 y = 4000 The solution of the equations is x = 2000, y = 4000. Therefore, the monthly incomesof the persons are Rs. 18,000 and Rs. 14,000, respectively.

works.Example 11 The ratio of incomes of two persons is 9: 7 and the ratio of theitexpenditures is 4 : 3. If each of them manages to save 2000 per month, find theirmonthly incomes.

Answer»

Denote the incomes of the two person by 9x and 7x and their expenditures by 4y and 3y respectively.

Then the equations formed in the situation is given by:

9x – 4y = 2000 ... (1)

7x – 3y = 2000 ... (2)

Step 1: Multiply Equation (1) by 3 and Equation (2) by 4 to make the coefficients ofy equal. Then you get the equations:

27x – 12y = 6000 ... (3)

28x – 12y = 8000 ... (4)

Step 2: Subtract Equation (3) from Equation (4) to eliminate y, because the coefficients of y are the same. So,you get

(28x – 27x) – (12y – 12y) = 8000 – 6000

x = 2000

Step 3: Substituting this value of x in (1),

9(2000) – 4y = 2000

y = 4000

The solution of the equations is x = 2000, y = 4000.

Therefore, the monthly incomesof the persons are Rs. 18,000 and Rs. 14,000, respectively.