Question

A certain family has a husband, wife, son, and daughter. All together they are 68 years old. The husband is 3 years older than the wife, and the son is 3 years older than the daughter. Four years ago, all together the family was 54 years old. How old is the husband now?

Answer 1

`\large \boxed{\sf \bf \ \ 32 \ \ }`

Explanation:

Hello, please consider the following.

We know that "All together they are 68 years old." and "Four years ago, all together the family was 54 years old."

If all the family was alive four years ago, it means that four years ago the sum of their ages was 68 - 4 - 4 - 4 - 4 because they are four members, so it gives 68 - 16 =52 which is different from 54, right ?

It means that we have the daughter in between, 54- 52 = 2, so the daughter's age is 2, and then the son's age is 5.

The husband is 3 years older than the wife. Let's note W the wife's age, we can write W + 3 + W + 5 + 2 = 68

2 W + 10 = 68

2 W = 68 - 10 = 58 so W = 29

and then the husband's age is 29 + 3 = 32.

And we can verify that 32 + 29 + 5 + 2 = 68, and four years ago, 28 + 25 + 1 + 0 = 54.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer 2

32

Explanation:

Everyone added together = 68

Four years ago, they were 68 -16 = 52

But the question told 54 years.

So there was a girl who was 2 years.

Girl = 2

Boy = 2 +3 = 5

Husband = 3 +w

Wife =w

3 +w +w + 5 + 2 = 68

10 + 2w = 68

2w = 58

w = 29

Wife = 29

Husband = 29 +3 =32

Husband = 32 years