Question

a gannet flies 24 1/2 ft above sea level. it increases its elevation by 5ft. then it dives and changes its elevation by - 47 2/3. after it dives, what is the gannets elevation relative to sea level? show your work.

Answer 1

So after the dive, the gannet's elevation relative to sea level is

`$-18 (1)/(6)$`

To determine the gannet's elevation relative to sea level after it dives, follow these steps:

Step 1:Convert the mixed numbers to improper fractions.

`\[ 24 (1)/(2) = (2 * 24 + 1)/(2) = (48 + 1)/(2) = (49)/(2) \]`

`\[ -47 (2)/(3) = -(3 * 47 + 2)/(3) = -(141 + 2)/(3) = -(143)/(3) \]`

Step 2: Increase the elevation by 5 ft.

`\[ (49)/(2) + 5 = (49)/(2) + (10)/(2) = (49 + 10)/(2) = (59)/(2) \]`

Step 3: Add the change in elevation due to the dive.

`\[ (59)/(2) + (-(143)/(3)) \]`

To add these fractions, they need a common denominator. The least common denominator (LCD) for 2 and 3 is 6.

Step 4: Convert both fractions to have the common denominator of 6.

`\[ (59)/(2) * (3)/(3) = (177)/(6) \]`

`\[ -(143)/(3) * (2)/(2) = -(286)/(6) \]`

Step 5: Now add the fractions.

`\[ (177)/(6) + (-(286)/(6)) = (177 - 286)/(6) = -(109)/(6) \]`

This is the gannet's elevation in feet as an improper fraction.

Step 6: Convert the improper fraction back to a mixed number.

`\[ -(109)/(6) = -18 (1)/(6) \]`

Answer 2

A gannet initial elevation is 24 1/2 ft

it increases its elevation by 5ft then the elevation is 5 + 24 1/2 = 29 1/2 ft

now it dives 47 2/3 ft

so the final elevation is,

`29(1)/(2)-47(2)/(3)`
`=(59)/(2)-(143)/(3)`

`=(177-286)/(6)=(-109)/(6)`

so its elevation below to the sea level is -109/6 or -18 1/6 ft