Equation worded problem.

Question

I am Richard and I am x years old. Father is three times my age, mother is two years younger than my father, my sister is one year older than me. The total of our ages is 103, Form an equation and solve it to find all the families age.

Answer 1

Maisy,

 

Richard's age is x

His father's age is 3x

His mother's age is 3x - 2

His sister's age is x + 1.

 

Add these together and set equal to 103:

 

x + 3x + (3x - 2) + (x + 1) = 103.

 

To solve, first combine like terms:

 

8x - 1 = 103.

 

Then, separate the 8x from the -1 by adding 1 to both sides:

 

8x = 104.

 

Next, divide by 8:

 

x = 104/8 = 13.

 

This means Richard's age is 13. You can get the ages of the rest of his family by plugging x = 13 into the age formulas above and simplifying them:

 

His father's age is 39

His mother's age is 37

His sister's age is 14.

 

To check, add the four ages together:

 

13 + 39 + 37 + 14 = 103. It is correct!