Question

Four friends were born in consecutive years. The sum of their ages is 94. What is the age of the oldest friend?

Answer 1

Hello,

We don't need algebra to solve this.

I suppose the ages are 1,2,3,4
Their sum is 1+2+3+4=10.
To obtain 94 we must add 94-10=84 for 4 persons =>84/4=21 to each

Ages are
1+21=22
2+21=23
3+21=24
4+21=25

But if really want an algebric resolution:

Let's x the age of the youngest
x+1,x+2,x+3 the others.

x+(x+1)+(x+2)+(x+3)=94
==>4x+6=94
==>4x=88
==>x=22
Ages are 22,23,24,25.

The oldest friend is 25 years old.

Answer 2

Answer: 25 years

Explanation:

Let x, x+1, x+2, x+3 are the ages of four friends which were born in consecutive years.

Now, according to the question

`x+(x+1)+(x+2)+(x+3)=94\\\\\Rightarrow4x+6=94\\\\\Rightarrow4x=94-6\\\\\Rightarrow4x=88\\\\\Rightarrow\ x=(88)/(4)\\\\\Rightarrow\ x=22`

Now, the age of the oldest friend
`= x+3=22+3=25\text{ years}`

Hence, the age of the oldest friend is 25 years.