Math, asked by nirmaldarrick3398, 1 year ago

Sum of three times the daughter's age and the mother's age is 70, and the sum of three times the mother's age and the daughter's age is 98.

Answers

Answered by Seth18
2

Hope this method is convenient for you.

Attachments:
Answered by hukam0685
0

Age of daughter is 14 years and age of mother is 28 years.

Given:

  • Sum of three times the daughter's age and the mother's age is 70,
  • and the sum of three times the mother's age and the daughter's age is 98.

To find:

  • Find the age of mother and daughter.

Solution:

Concept to be used:

  • Assume the age of mother and daughter.
  • Form pair of linear equations in two variables.
  • Solve equations to find ages of both.

Step 1:

Let the age of daughter is x years and that of mother is y years.

So,

According to the first case;

\bf 3x + y = 70  \: ...eq1\\

and

\bf x + 3y = 98 ...eq2\\

Step 2:

Add and subtract both equations.

4x + 4y = 168 \\

or

\bf x + y = 42...eq3 \\

and

2x - 2y =  - 28 \\

or

\bf x - y =  - 14...eq4 \\

Step 3:

Solve eq3 and eq4

x + y = 42 \\ x - y =  - 14 \\  -  -  -  -  -  -  -  \\ 2x = 28 \\

or

\bf \red{x = 14} \\

put the value of x in eq 3.

14 + y = 42 \\

or

y = 42 - 14 \\

or

\bf \red{y = 28} \\

Thus,

Age of daughter is 14 years and age of mother is 28 years.

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