Juan is 8 years older than his sister. In 3 years, he will be twice as old as she will be then.?

Question

How old are they now?

Answer 1

Hi,


Now....in 3 years
x+8........x+11......Juan
x.............x+3.........sister

x + 11 = 2(x+3)
x + 11 = 2x + 6
x + 5 = 2x
5 = x <== sister's age
13 <== Juan's age

I hope that helps!! :-)

Answer 2

OK

Juan = x+8
Juan sister = x

x+8+3 = 2 (x +3)
x + 11 = 2x +6
5 = x

If x =5, Juan's sister is 5. Juan is 13.

Let's check

Today he is 8 years older than his sister? True.
In three years he will be 16 and she will be 8 which means he will be twice her age.

Hope this helps.

Answer 3

Let x = the sister's age

x + 8 = Juan's age

(x + 8) + 3 = 2 (x + 3), that's in 3 years, now solve for x

x + 11 = 2x + 6

5 = x

The sister is 5, Juan is 13.

That's it!

Answer 4

Let J be Juan's age now
Let S be his sister's age now.

In 3 years their ages will be:
J + 3 and S + 3 respectively.

Equation 1: Juan is 8 years older than his sister.
J = S + 8

Equation 2: In 3 years, Juan will be twice as old as she will be then.
J + 3 = 2(S + 3)

Substitute in for J:
(S + 8) + 3 = 2(S + 3)

Simplify:
S + 11 = 2S + 6

Subtract 6 from both sides:
S + 5 = 2S

Subtract S from both sides:
5 = S

So his sister is 5.

J = S + 8
J = (5) + 8
J = 13

So Juan is 13 and his sister is 5
(In 3 years they will be 16 and 8, which is twice as old...)

Answer 5

Let J=Juan's age now, and S= his sister's age now,
Now J=S+8,
in 3 years J+3=2(S+3)

substituting:
S+8+3=2S+6, S+11=2S+6, S=5, which is his sister's age, and J=13 which is Juan's age.

Answer 6

Juan is 13 and his sister is 5

13+3=16

5+3 = 8

16 is two times 8

Answer 7

Let sister's age = x
Juan's age = x+8
In 3 years, sister's age = x+3
In 3 years, Juan's age=x+8+3=x+11
x+11=2(x+3)
x+11=2x+6
-x=-5
x=5 (sister's age)
x+8=13 (Juan's age)
check the answer by comparing their ages in the question.

Answer 8

let x equal juans sister's age
so juan will be 8+x
in three years it will be
3+8+x=2(x+3)
11+x=2x+6
x=5
so juan is 13 years old and his sister is 5 years old:D

Answer 9

When she is 8 years old he will be 16. So right now she is 5 and he is 13.

Answer 10

let Juan be x years old, his sister will be x-8

after 3 years

x+3 = 2(x-8+3)

x+3=2x-10

x=13

his sister is 5

Answer 11

We'll use X for Juan's years and Y for his sisters

first you have that

X-Y=8

in second case you have that

X+3=2*(Y+3)
you just sort it a little and you get
X+3=2Y+6
X-2Y=3

Now you put them together and you'll have a system

X-Y=8
X-2Y=3 /*-1 you multiply both sides of the second one with -1
__________
X-Y=8
-X+2Y=-3 + you add them together
__________
X-X+2Y-Y=8-3

Y=5 Now you use this result in the first equation and you'll get

X-5=8
X=13

You can check it and you'll get

X(13)-Y(5)=8 CHECK
X(13)-2Y(5)=13-10=3 CHECK

So the end results are

X=13 Juan is 13 years old
Y=5 his sister is 5

;)