SOLVING SYSTEM OF LINEAR EQUATIONS WORD PROBLEMS IN 2 VARIABLES

Problem 1 :

A fraction becomes 9/11, if 2 is added to both numerator and the denominator. If 3 be added to both the numerator and the denominator, the fraction becomes 5/6. Find the fraction.

Solution :

Let x/y be the required fraction

If 2 is added to both numerator and denominator the fraction becomes 9/11.

(x + 2)/(y+2)  =  9/11

11(x + 2)  =  9(y + 2)

11x + 22  =  9y + 18

11x – 9y  =  18 – 22

11x – 9y  =  -4 ------(1)

If 3 is added to both the numerator and the denominator it becomes 5/6.

(x + 3)/(y+3)  =  5/6

6(x + 3)  =  5(y + 3)

6x + 18  =  5y + 15

6x – 5y  =  15 - 18

6x – 5y  =  - 3 ------(2)

Solving (1) and (2), we get

                                               x  =  7

Substitute 7 for x in (1). 

(1)-----> 11(7) – 9y  =  -4

77 – 9y  =  -4

-9y  =  -81

y  =  9

Then, 

x/y  =  7/9

So, the required fraction is 7/9.

Problem 2 :

Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

Solution :

Let x be the age of Jacob and y be the age of his son.

5 years hence their ages will be

x + 5 and y + 5

x + 5  =  3(y + 5)

x + 5  =  3y + 15

 x – 3y  =  -5 + 15

 x – 3y  =  10 ------(1)

5 years ago, their ages were

x – 5 and y – 5

x – 5  =  7(y – 5)

x – 5  =  7y – 35

x – 7y  =  5 - 35

x – 7y  =  -30 ------(2)

(1) - (2) :

4y  =  40

y  =  10

Substitute 10 for y in (2).

(2)------> x - 7(10)  =  -30

x – 70  =  -30

x  =  40

Therefore,

age of Jacob's son  =  10

Age of Jacob  =  40

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. Power Rule of Logarithms

    Oct 04, 22 11:08 PM

    Power Rule of Logarithms - Concept - Solved Problems

    Read More

  2. Product Rule of Logarithms

    Oct 04, 22 11:07 PM

    Product Rule of Logarithms - Concept - Solved Problems

    Read More

  3. Quotient Rule of Logarithms

    Oct 04, 22 11:06 PM

    Quotient Rule of Logarithms - Concept - Solved Problems

    Read More