Question

The average amount of bacteria on the bathroom countertop is 452 bacteria per square inch. How many bacteria would you expect to find on a rectangular bathroom counter top that 1.5ft by 2ft. Round the answer to the highest place value

Answer 1

First, we need to convert units. In this case, we can convert feets into inches. Since we know that 1 ft=12 in, then we have

`1.5ft=1.5ft((12in)/(1ft))`

which is equal to

`\begin{gathered} 1.5ft=(1.5)(12)IN \\ 1.5ft=18IN \end{gathered}`

Similarly, for 2 ft we get

`\begin{gathered} 2ft=(2ft)((12In)/(1ft)) \\ 2ft=(2)(12In) \\ 2ft=24In \end{gathered}`

Now, we can compare the bacterias in both scenarios. By applying the rule of three, we have

`\begin{gathered} 452bacteria-----1in^2 \\ x---------(18)(24)in^2 \end{gathered}`

then, x is equal to

`\begin{gathered} x=((18)(24)(452))/(1) \\ x=(18)(24)(452) \\ x=195264\text{ bacteria} \end{gathered}`

that is, in an area of (18)(24)in^2 , there are 195,264 bacterias. By rounding to the highest place value, the answer is 200,000 bacterias.