Question

LOW TIDE The daily water level is recorded for seven

straight days at a tide station on the Big Marco River in
Florida. On which days is the water level higher than on
the previous day? On which days is it lower?
Sun Mon Tues. Wed. Thurs. Fri. Sat. -3/25, -7/20, -27/50, -13/20, -16/25, -53/100, -1/3​ for 10+ points

Answer 1

The smallest level was on Wednesday
`(-(13)/(20))`

The greatest level was on Sunday
`(-(3)/(25))`

Explanation:

The daily water level is recorded in the following table for seven straight days at a tide station on the Big Marco River in Florida.

`\begin{array}{ccccccc}\text{Sun}&\text{Mon}&\text{Tue}&\text{Wed}&\text{Thu}&\text{Fri}&\text{Sat}\\ -(3)/(25)&-(7)/(20)&-(27)/(50)&-(13)/(20)&-(16)/(25)&-(53)/(100)&-(1)/(3)\end{array}`

Rewrite all fractions with denominators 300:

`-(3)/(25)=-(3\cdot 12)/(25\cdot 12)=-(36)/(300)\\ \\-(7)/(20)=-(7\cdot 15)/(20\cdot 15)=-(105)/(300)\\ \\-(27)/(50)=-(27\cdot 6)/(50\cdot 6)=-(162)/(300)\\ \\-(13)/(20)=-(13\cdot 15)/(20\cdot 15)=-(195)/(300)\\ \\-(16)/(25)=-(16\cdot 12)/(25\cdot 12)=-(192)/(300)\\ \\-(53)/(100)=-(53\cdot 3)/(100\cdot 3)=-(159)/(300)\\ \\-(1)/(3)=-(1\cdot 100)/(3\cdot 100)=-(100)/(300)`

So, the table is

`\begin{array}{ccccccc}\text{Sun}&\text{Mon}&\text{Tue}&\text{Wed}&\text{Thu}&\text{Fri}&\text{Sat}\\ -(36)/(300)&-(105)/(300)&-(162)/(300)&-(195)/(300)&-(192)/(300)&-(159)/(300)&-(100)/(300)\end{array}`

The smallest level was on Wednesday
`(-(13)/(20))`

The greatest level was on Sunday
`(-(3)/(25))`