Question

Please answer this question

Four years ago, the sum of the ages of a mother and her two daughters was x years,

then after two years, the sum of their ages becomes ___ years.​

Answer 1

Answer:

After two years, the sum of their ages becomes $x$ + 6  years.​

Step-by-step explanation:

Four years ago, the sum of the ages of a mother and two daughters was $x$ years.

Ah... that's good, they told you their age was $x$ years. Because you will have to make the unknown $x$ anyways.

Let's go through the question.

Four years ago, the sum of the ages of a mother and her two daughters was x years,

Four years ago. So the formula would be the number, minus 4.

Then, the sum of the ages of a mother and her two daughters was $x$ years.

Which means :

( Mother + Daughter 1 + Daughter 2 ) - ( 4 ( 3 ) ) =  $x$

Why 3?

Because there is a Mother, and 2 daughters.

And also because it is four years ago, therefore by combining the three people, the total years should have 4 multiplied by 3.

Now the formula :

( Mother + Daughter 1 + Daughter 2 ) - ( 4 ( 3 ) ) =  $x$

( Mother + Daughter 1 + Daughter 2 ) - 12 =  $x$

Our formula is ( Mother + Daughter 1 + Daughter 2 ) - 12 =  $x$.

Then forward to the last part of the question.

then after two years, the sum of their ages becomes ___ years.​

After two years, mind you. So, which means, let's say four years ago, it's 2016. Now they want you to calculate their ages AFTER TWO YEARS. Which is, after two years, 2020, added by 2.

So they want you to calculate the total of their ages in 2022.

It's confusing, since there are no numbers, but it's possible.

By using this formula ( Mother + Daughter 1 + Daughter 2 ) - 12 =  $x$

Add 12 to get the formula for this year  ( 2020 )

So, it would be ( Mother + Daughter 1 + Daughter 2 )  =  $x$ + 12

Another 2 years.

Remember, there are 3 people, so you would have to multiply 2 ( 3 ).

Why?

Now it would mean ( Mother's Age + 2 ) + ( Daughter 1 + 2 ) + ( Daughter 2 + 2 ) = $x$ + 12

Instead of writing so long, why not :

( Mother's Age ) + ( Daughter 1 ) + ( Daughter 2 ) + 6 = $x$ + 12 ?

Now I want the years.

So, it would be :

( Mother's Age ) + ( Daughter 1 ) + ( Daughter 2 ) + 6 ( -6 ) = $x$ + 12 ( -6 )

( Mother's Age ) + ( Daughter 1 ) + ( Daughter 2 ) = $x$ + 6

So, therefore, after two years, the sum of their ages becomes  $x$ + 6 years.

Want to proof my answer right?

Fill in the ages.

Any random number.

Let's say,

mother's age = 30

Daughter 1's age = 14

Daughter 2's age = 10

By using this year's ( 2020 ) formula :

( Mother + Daughter 1 + Daughter 2 ) =  $x$

Or, let's say :

$x$ = ( Mother + Daughter 1 + Daughter 2 )

  = ( 30 + 14 + 10 )

  = 54

In 2020, their total age is 54.

Now towards 2022 :

First formula :

( Mother's Age + 2 ) + ( Daughter 1 + 2 ) + ( Daughter 2 + 2 ) = $x$ + 12

OR

$x$ + 12 = ( Mother's Age + 2 ) + ( Daughter 1 + 2 ) + ( Daughter 2 + 2 )

        = ( 30 + 2 ) + ( 14 + 2 ) + ( 10 + 2 )

        = 32 + 16 + 12

        = 60

Second Formula :

( Mother's Age ) + ( Daughter 1 ) + ( Daughter 2 ) + 6 = $x$ + 12

$x$ + 12 = ( Mother's Age ) + ( Daughter 1 ) + ( Daughter 2 ) + 6

        = ( 30 + 14 + 10 ) + 6

        = ( 54 ) + 6

        = 60

Two years later, their total age is 60.

To find present ( 2020 ), deduct 6 to their total ages :

60 - 6 = 54

And 54 is their total present age : similar to the formula just now!

$x$ = ( Mother + Daughter 1 + Daughter 2 )

  = ( 30 + 14 + 10 )

  = 54

So therefore, the formula ( Mother's Age ) + ( Daughter 1 ) + ( Daughter 2 ) = $x$ + 6

So, the answer :

After two years, the sum of their ages becomes $x$ + 6  years.​

HOPE THIS ANSWER HELPED :)