Question #b9e5a

2 Answers

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 = 4M

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(M-5)

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.

7M - 30 = 4M

3M - 30 = 0

3M = 30

M = 10

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

5) Double check by substituting.

M = 10

F = 4M = 40

F - 5 = 35

M - 5 = 5

5 xx 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 4x

Five years ago, they were both younger by 5 years

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

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

Write this as an equation.

7(x-5) = 4x-5

7x -35 = 4x-5

7x-4x = 35-5

3x = 10

x =10

She is 10 now and he is 40

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

7 xx 5 = 35