Question

Jonathon has opened his 50th Phoenix Sporting Goods Store in the US. He is trying to make sure his stores are cheaper than Model's. His price for jerseys like Anthony Raez's Arsenal soccer jersey is 4(1/2J - 5) Meanwhile, Model's price is 2J + 10. Will their prices ever be the same, always the same, or is there a value for J where they will be the same?

A. They will always be the same price.
B. They never will be the same.
C. They will be the same when J = 30.

Answer 1

The prices at Jonathan's Phoenix Sporting Goods Stores and Model's will never be the same, as the equation set to determine the equal price point yields a false statement, showing that there is no value for J where both prices will match.

Step-by-step explanation:

The question asks to determine whether the prices of jerseys at Jonathan's Phoenix Sporting Goods Stores and Model's will ever be the same, and if so, at what value of J. Jonathan's price function for the jerseys is 4(1/2J - 5) and Model's price is 2J + 10. To establish when the prices are the same, we need to set the two functions equal to each other and solve for J:

• 4(1/2J - 5) = 2J + 10
• 2J - 20 = 2J + 10
• -20 = 10 (This statement is false; hence, there are no values of J that will make the prices the same.)

Therefore, they never will be the same price, which corresponds to option B.