Question

Scott’s age and his mother’s age is 45. In 5 years’ time, three times Scott’s age less9 will be the same as his mother’s age. Find the present ages of Scott and his mother.

Answer 1

Mother is presently 34

Scott is 11

Explanation:

Let the mother's age = x

Let the son's age = y

First Equation

x + y = 45

Second equation

3*(x + 5) - 9 = y+5 Add 9 to both sides

3(x + 5) = y + 5 + 9

3(x + 5) = y + 14 Remove the brackets

3x + 15 = y + 14 Subtract 14 from both sides

3x + 15 - 14 = y

3x + 1 = y

Put the first equation into the second equation

x + y = 45 Subtract y from both sides

y = 45 - x

Put this value for y into the second equation's results.

3x + 1 = 45 - x Add x to both sides

3x + x + 1 = 45

4x + 1 = 45 Subtract 1 from both sides

4x = 45 - 1

4x = 44 Divide by 4

x = 44/4

x = 11

x + y = 45

11 + y = 45

y = 34