## 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

Question

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?

in progress 0
2 weeks 2021-09-09T16:24:13+00:00 2 Answers 0

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

2. 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