# Question b9e5a

Feb 22, 2017

The Father is now $40$ and Mary is $10$.

#### Explanation:

Let us say the current Mary is $M$ and her current father is $F$.

1) In the present:

$F = 4 M$

Mary’s father is four times as old as Mary.

2) Using the terms above, the equation of their age $5$ years ago is this:

$F - 5 = 7 \left(M - 5\right)$

The father is $5$ years younger and is $7$ times older than Mary was $5$ years ago.

3) Remove the brackets from the previous equation, simplify it and bring it into the terms of $F$.

i) " "F - 5 = 7M - 35

ii) " "F = 7M - 30#

4) Piece it all together.

$7 M - 30 = 4 M$

$3 M - 30 = 0$

$3 M = 30$

$M = 10$

We already know that $F = 4 M$, and we just worked out that F also $= 7 M - 30$. This means $4 M$ and $7 M - 30$ is the same. After working it all out, we see $M = 10$.

5) Double check by substituting.

$M = 10$

$F = 4 M = 40$

$F - 5 = 35$

$M - 5 = 5$

$5 \times 7 = 35$

It all works out...

6) All Done! I hope I helped.

Jul 29, 2017

She is $10$ now and he is $40$

#### Explanation:

There are two people: Mary and her Father

and two periods of time: present and $5$ years ago.

Write an expression for each person for each period of time:

Mary is younger, so let her present age be $x$
Her father is $4$ times older, so his present age is $4 x$

Five years ago, they were both younger by $5$ years

Mary's age was $x - 5$
Her father was $4 x - 5$

However, $5$ years ago, he was $7$ times as old as she was.

Write this as an equation.

$7 \left(x - 5\right) = 4 x - 5$

$7 x - 35 = 4 x - 5$

$7 x - 4 x = 35 - 5$

$3 x = 10$

$x = 10$

She is $10$ now and he is $40$

$5$ years ago .... She was $5$ and he was $35$

$7 \times 5 = 35$