Question

Ann is 18 years older than son. one year ago she was 3 times as old as her son. How old are they now​

Answer 1

Answer:

HI MATE !

SOLUTION :- ⬇️

Let s be the son, and s+18 be Ann. Then:

3(s-1)=s+18–1

3s-3=s+17

2s=20

s=10

The son is 10; Ann is 28

OR

Ann is 18 years older than her son.

A = S + 18

A year ago, she was 3 times her son's age.

We have to say A-1 and S-1 to represent their ages 1 year ago.

A-1 = 3*(S-1)

A-1 = 3S -3

A = 3S -2

We now have A defined by two equations.

S+18 = 3S-2

Subtract S from both S

18 = 2S-2

Add 2 to both sides

20 = 2S

2S = 20

Divide both sides by 2

S = 10, so the son is 10 years old.

Looking back at the setup equations.

A = S + 18

A = 10 + 18 = 28, so Ann is 28.

How old were they last year?

S = 10-1 = 9

A = 28-1 = 27

To check, was Ann 3 times as old as her son a year ago?

3*9 = 27

Hope my answer helps you Dear.... ✌️

☺️

Answer 2

Ann is 28 years old and her son is 10 years old

Given :

• Ann is 18 years older than son.

• One year ago she was 3 times as old as her son

To find :

Present age of Ann and her son

Solution :

Step 1 of 2 :

Form the equation to calculate present age of Ann and her son

Since Ann is 18 years older than son

Let present age of Ann = x years and present age of her son = (x - 18) years

One year ago age of Ann = (x - 1) years and age of her son = (x - 19) years

By the given condition

$\displaystyle \sf (x - 1) = 3(x - 19)$

Step 2 of 2 :

Calculate present age of Ann and her son

$\displaystyle \sf (x - 1) = 3(x - 19)$

$\displaystyle \sf{ \implies }x - 1 = 3x - 57$

$\displaystyle \sf{ \implies }3x - x = 57 - 1$

$\displaystyle \sf{ \implies }2 x = 56$

$\displaystyle \sf{ \implies } x = 28$

Present age of Ann = x = 28 years

Present age of her son

= (x - 18) years

= 28 - 18 years

= 10 years

Hence Ann is 28 years old and her son is 10 years old

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