Question

In City​ A, the temperature rises 4(degrees)F from 8 A.M. To 9 A.M. Then the temperature drops 7F from 9 A.M. To 10 A.M. In City​ B, the temperature drops 6F from 8 A.M. To 9 A.M. Then the temperature drops 2F from 9 A.M. To 10 A.M. Write an expression that represents the change in temperature from 8 A.M. To 10 A.M. For each city. Simplify and interpret each sum. Use pencil and paper. Which city has the greater change in​ temperature?

Answer 1

City A:

`A - 3`

City B:

`B - 8`

City B has a greater change in temperature.

Explanation:

City A:

Let the initial temperature of city A at 8 AM =
`A\ ^\circ F`

Temperature change from 8 AM to 9 AM: 4
`^\circ F` rise

Temperature at 9 AM =
`(A+4)\ ^\circ F`

Temperature change from 9 AM to 10 AM: 7
`^\circ F` drop

Temperature at 9 AM =
`(A+4 -7 )\ ^\circ F = (A-3)\ ^\circ F`

Total change in temperature =
`(A - 3) - A = 3\ ^\circ F` drop

City B:

Let the initial temperature of city B at 8 AM =
`B\ ^\circ F`

Temperature change from 8 AM to 9 AM: 6
`^\circ F` drop

Temperature at 9 AM =
`(B-6)\ ^\circ F`

Temperature change from 9 AM to 10 AM: 2
`^\circ F` drop

Temperature at 9 AM =
`(B-6 -2 )\ ^\circ F = (B-8)\ ^\circ F`

Total change in temperature =
`(B - 8) -B = 8\ ^\circ F` drop

Therefore, the answer is:

City B has a greater change in temperature.