# Will is 5 years older than Amy. After 3 years, Will will be twice Amy's age. How old are they now?

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First we will assume that Will's age now is W

And Amy's age now is A

But Will is 5 years older

==> W = A+5.....(1)

After three years:

Will's age will be W+3

Amy's age will be A+3

But Will will be twice Amy's age:

==> W+3 = 2(A+3)

==> W+3 = 2A + 6 .....(2)

Now from (1) substitute with W= A+5:

==> A+5 +3 = 2A +6

==> A+8 = 2A +6

==> A = 2 years

==> W = A+5 = 2+5 = 7 years old.

To check:

After 3 years , Amy will be 5 and Will will be 10 which is twice Amy's age.

We'll note the Will's age with a and Amy's age with b.

a=b+5 (1)

After 3 years, their ages will be:

a+3 = 2(b+3) (2)

We'll add 3 both sides, to the relation (1):

a+3 = b+5+3

a+3 = b+8

But, from relation (2), a+3 = 2(b+3), so:

b+8 = 2(b+3)

b+8 = 2b + 6

2b-b = 8-6

b = 2

a = b+5

a = 2+5

a = 7

**So, Amy is 2 years old and Will is 7 years old.**

let Amy's age be x

Will's age = x + 5

After 3 years,

Amy's age = x+3

Will's age = x+5+3 = x+8

According to problem,

Will's age = 2Amy's age

x + 8 = 2(x + 3)

x+8 = 2x + 6

x = 2

therefore,

Amy's age = x = 2

Will's age = x+5 = 2+5 = 7

Let:

Age of Will = x, and

Age of Amy = y

Then as per the conditions stated in the question:

x = y + 5

x - y = 5 ... (1)

x + 3 = 2(y + 3)

x + 3 = 2y + 6

x - 2y = 6 - 3

x - 2y = 3 ... (2)

Subtracting equation (2) from equation (1) we get:

x - x - y + 2y = 5 - 3

y = 2

Substituting value of y in equation (1) we get:

x - 2 = 5

x = 5 + 2 = 7

Answer:

Age of Will = 7 years

Age of Amy = 2 years

Let the ages of will and amy be x+5 and x. Now their age relation is: After 3 years the age reatin becomes:

(x+5)+3 = 2(x+3).

x+8 = 2x+6. Or

8-6 = 2x-x.

2= x.

So Amy is 2years and Will 7years.

After 3 years Amy is 2+3 = 5 and Will 7+3 = 10 which is twice Amy's age