Question

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.

Answer 1

Hope this method is convenient for you.

Answer 2

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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