Answer to Question #95932 in Algebra for raquel amaro

Question

Jake owns two gas stations in town. The projected revenue of the first gas station for the next 12 months is
0.3t2 + 150t (0 ≤ t ≤ 12)
thousand dollars t months from now. The projected revenue of the second gas station for the next 12 months is
0.4t2 + 250t (0 ≤ t ≤ 12)
thousand dollars t months from now. Find an expression that gives the amount by which the revenue of the second gas station will exceed that of the first gas station in month t (0 ≤ t ≤ 12).

Answer 1

Finding of an expression of revenue

We need to find an expression that gives the amount by which the revenue of the second gas station will exceed that of the first gas station in month t

Solution:

revenue of the first gas station = = (0.3 t² + 150 t)

revenue of the second gas station = (0.4 t² + 250 t)

Example: If a person A has the amount x and the another person B has amount y,

an expression that gives the amount of person B has exceed by "y - x"

Required expression = revenue of the second gas station - revenue of the first gas station

= (0.4 t² + 250 t ) - ( 0.3 t² + 150 t)

open the parenthesis and combine the like terms

= ( 0.4 t² - 0.3 t² ) + ( 250 t - 150 t)

in the first parenthesis, t² is common, factor it

In the second parenthesis, t is common, factor it

Required expression = ( 0 .4 - 0.3 ) t² + ( 250 - 150 ) t

= 0.1 t² + 100 t

Answer

an expression that gives the amount by which the revenue of the second gas station will exceed that of the first gas station in month t = 0.1 t² + 100 t