Question

Dad, Anna, and Todd are walking in a city park together. While dad made 3 steps, Anna made 5 steps. For every 3 of Anna's steps, Todd made 5 steps. Anna and Todd calculated that they did 400 steps together. How many steps did dad make during that period?

Answer 1

Dad made 90 steps during that period.

Explanation:

Let x,y,z be the steps made by dad,Anna and Todd.

Given that while dad made 3 steps, Anna made 5 steps.

That is
`(x)/(y)= (3)/(5)`

`y=(5x)/(3)`

And for every 3 steps Anna made, Todd made 5 steps.

That is
`(y)/(z)= (3)/(5)`

`z=(5y)/(3) =(5((5x)/(3)) )/(3) =(25x)/(9)`

It is also given that total number of steps made by Anna and Todd is 400.

That is y+z=400

let us plugin y and z in terms of x.

`(5x)/(3) +(25x)/(9) =400`

`(15x)/(9) +(25x)/(9)=400`

`(40x)/(9)=400`

`x=400X(9)/(40) =90steps`

Hence Dad made 90 steps during that period.