Question

Aaron is three times as old as his son. In ten years Aaron will be twice as old as his son. How old is Aaron?​

Answer 1

Answer:

Aaron (A)=30 years old currently. (Aaron's son (S)=10 years old currently)

PREMISES

3S+10=2(S+10)

ASSUMPTIONS

Let A=Aaron's “current” age (3S in terms of his son's age)

Let S=Aaron's son's “current” age (S)

CALCULATIONS

3S+10=2(S+10)

3S+10=2S+20

(3S-2S)+10=(2S-2S)+20

S+10=0+20

S+(10–10)=20–10

S+0=10

S=

10 years old

and,

if S=10 years old, then

A=3S (Aaron's “current” age in terms of his son's age)

A=3(10)

A=

30 years old

Step-by-step explanation:

Answer 2

Aaron is 30 years old

Given :

• Aaron is three times as old as his son.

• In ten years Aaron will be twice as old as his son

To find :

The present age of Aaron

Solution :

Step 1 of 2 :

Form the equation to calculate present age of Aaron

Let present age of Aaron's son is x years

Since Aaron is three times as old as his son

∴ Present age of Aaron = 3x years

Now in ten years Aaron's son will be (x + 10) years old and Aaron will be (3x + 10) years old

Since in ten years Aaron will be twice as old as his son

By the given condition

$\displaystyle \sf (3x + 10) = 2(x + 10)$

Step 2 of 2 :

Calculate present age of Aaron

$\displaystyle \sf (3x + 10) = 2(x + 10)$

$\displaystyle \sf{ \implies }3x + 10 = 2x + 20$

$\displaystyle \sf{ \implies }3x - 2x = 20 - 10$

$\displaystyle \sf{ \implies }x = 10$

Present age of Aaron's son = x = 10 years

Present age of Aaron = 3x = 3 × 10 = 30 years

Hence Aaron is 30 years old

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