Tim is 4 years older than one-third of Juan's age. In 10 years, Juan will be 6 years older than twice as old as Tim is now. How old is each now?

Answer: Tim is 8 years old.

Juan is 12 years old

Step-by-step explanation:

Let x represent the present age of Tim.

Let y represent the present age of Juan.

Tim is 4 years older than one-third of Juan's age. This is expressed as

x = y/3 + 4

In 10 years, Juan will be 6 years older than twice as old as Tim is now. This is expressed as

2 (x + 10) = (y + 10) + 6

2x + 20 = y + 16

2x - y = 16 - 20

2x - y = - 4

2y/3 + 8 - y = 4

2y + 24 - 3y = 12

2y - 3y = 12 - 24

- y = - 12

y = 12

Substituting y = 12 into x = y/3 + 4, it becomes

12/3 + 4

x = 4 + 4

x = 8

Juan's current age = 12

Tim's current age = 8

Step-by-step explanation:

Let x = Juan's current age; x+10=Juan's age in 10 years

Then (1/3) x+4=Tim's current age;

Now we are told that:

x+10=2{ (1/3) x+4}+6 eliminate brackets

x+10 = (2/3) x+8+6 = (2/3) x+14 multiply both sides by 3

3x+30=2x+42 subtract 30 and 2x from both side s

3x-2x+30-30=2x-2x+42-30 collect like terms

Juan's current age: x=12

Tim's current age: (1/3) x+4 = (1/3) * 12+4=8

4 years older than 1/3 of Juan's age = (1/3) * 12+4=8

8=8

In 10 years, Juan will be 6 years older than twice as old as Tim is now.

12+10=22

2*8+6=22

22=22