Question

a person walked x feet an then 1/4 that length again. two students wrote different equations to represent this relationship. y=x+ 1/4x and y=5/4 x explain why both are true

Answer 1

Let x be the lenght, then he walked

$y=x+\frac{1}{4}x$

By combining similar terms, we get

$y=(1+\frac{1}{4})x$

now, since

$1+\frac{1}{4}=\frac{4}{4}+\frac{1}{4}=\frac{4+1}{4}=\frac{5}{4}$

we can write

$y=\frac{5}{4}x$

thats why both equations express the same sentence.