Question

Sophia mandy and alexis are cousins sophia is 3/4 as tall as mandy. alexis is 5/6 as tall as mandy . what is the difference in height between sophia and alexis id mandy is 5 feet tall

1/12
5/12
4 1/6
3 3/4

Answer 1

`(5)/(12)` feet

Explanation:

Let height of mandy be m, sophia be s, and alexis be a

"sophia is 3/4 as tall as mandy":

`s=(3)/(4)m`

"alexis is 5/6 as tall as mandy":

`a=(5)/(6)m`

Since mandy is 5 feet, we plug in 5 into m in both of the equations to find height of alexis and sophia.

Sophia =
`(3)/(4)(5)=(15)/(4)`

Alexis =
`(5)/(6)(5)=(25)/(6)`

Difference in height of Alexis and Sophia is
`(25)/(6)-(15)/(4)=(5)/(12)` feet