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

Answer:

Dad made 90 steps during that period.

Step-by-step 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 $\frac{x}{y}= \frac{3}{5}$

           $y=\frac{5x}{3}$

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

That is $\frac{y}{z}= \frac{3}{5}$

            $z=\frac{5y}{3} =\frac{5(\frac{5x}{3}) }{3} =\frac{25x}{9}$

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.

       $\frac{5x}{3} +\frac{25x}{9} =400$

        $\frac{15x}{9} +\frac{25x}{9}=400$

       $\frac{40x}{9}=400$

       $x=400X\frac{9}{40} =90steps$

Hence Dad made 90 steps during that period.