Question #b9e5a

2 Answers

Answer:

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

Answer:

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#