Question

In 1974 a mother was 6 times as old as her daughter. If the mother turned 50 in the year 2000, in what year was the mother double her daughter’s age?

This is in the topic of linear equations and please provide an explanation. (The working out)

Answer 1

1990

Explanation:

Since the mother was 50 years old in 2000, she was 50 - (2000-1974) = 50 - 26 = 24 years old in 1974.

Hence, the daughter was 24/6 = 4 years old in 1974.

In "x" years after 1974, the daughter will be 4+x years old, while the mother will be 24+x years old.

We need to find "x" from the equation

2(4 + x) = 24+x.

8 + 2x = 24 + x,

x = 24 - 8 = 16.

1974 + 16 = 1990.

Answer In 1990 the mother doubles her daughter's age

Check In 1990 mother's age is/was 24 + 16 = 40 years.

In 1990 the daughter's age is/was 4 + 16 = 20 years.

Answer 2

In the year 2000 the mother was 50 so that means that in the year 1974 she was 24. If in 1974 she was 6x as old as her daughter then her daughter was 4 years old. Her daughter is 30 in the year 2000 so the year the mothers age was double her daughters age is before 2000 and after 1974. But since we know that in 2000 mom was 50 and daughter is 30 we can take 10 years from both to have 40 and 20. 40 is double of 20 so
In the year 1990 the mother was 40, and therefore double her daughters age, who was 20.