Question

Gabriella is 7 years older than Ben. Next year she will be 1 year more than twice as old as he will be. How old are they now?
(I need the answer ASAP, thank you :))

Answer 1

Step-by-step explanation:

Given:-

Gabriella is 7 years older than Ben. Next year she will be 1 year more than twice as old as he will be.

To find:-

How old are they now?

Solution:-

Let the present age of Ben be X years

Then , The present age of Gabriella

= 7 years older than Ben

= (X+7) years

Age of Ben next year = (X+1) years

Age of Gabriella next year

= (X+7)+1

= (X+8) years

According to the given problem

Next year she will be 1 year more than twice as old as he will be

=>Gabriella age = 2× age of Ben +1

=>(X+8) = 2(X+1)+1

=>X+8 = 2X+2+1

=>X+8 = 2X+3

=>8-3 = 2X-X

=>5 = X

=>X = 5

Present age of Ben = 5 years

Present age of Gabriella = X+7 = 5+7 = 12 years

Answer:-

Present age of Ben = 5 years

Present age of Gabriella = 12 years

Check:-

Age of Gabriella = 12 years

= 5+7 years

=>7 years older than Ben

and

Next year their ages will be

12+1 = 13 years and 5+1 = 6 years

Gabriella age = 13 years

=>(2×6)+1

=>Twice the age of Ben +1

Verified the given relations

Answer 2

Given Question :-

• Gabriella is 7 years older than Ben. Next year she will be 1 year more than twice as old as he will be. How old are they now?

Answer

Given :-

• Gabriella is 7 years older than Ben.

• Next year she will be 1 year more than twice as old as he will be.

To Find :-

• How old are they now?

$\large\underline{\bold{Solution :- }}$

$\begin{gathered}\begin{gathered}\bf \:Let \: the \: present \: age \: of \: \begin{cases} &\sf{Ben \: be \: x \: years} \\ &\sf{Gabriella \: be \: x + 7 \: years} \end{cases}\end{gathered}\end{gathered}$

So,

• After one year,

$\begin{gathered}\begin{gathered}\bf \ \: age \: of \: - \begin{cases} &\sf{Ben \: be \: x + 1\: years} \\ &\sf{Gabriella \: be \: x + 8 \: years} \end{cases}\end{gathered}\end{gathered}$

$\large \underline{\tt \:{ According \: to \: statement }}$

Gabriella will be 1 year more than twice as old as Ben will be.

$\rm :\implies\:x + 8 = 2(x + 1) + 1$

$\rm :\implies\:x + 8 = 2x + 2 + 3$

$\rm :\implies\:x + 8 = 2x + 3$

$\rm :\implies\:x = 5$

$\begin{gathered}\begin{gathered}\bf \:Hence \: the \: present \: age \: of \: \begin{cases} &\sf{Ben \: be \: 5 \: years} \\ &\sf{Gabriella \: be \: 5+7 = 12\: years} \end{cases}\end{gathered}\end{gathered}$