Question

for problems 1–6, use the read-represent-solve-summarize routine to find the answer. 1. kabir paid an entrance fee of $5 plus an additional $0.75 per game at a local arcade. the next week, he and a friend went to another arcade where kabir paid $1.25 per game, but there was no entrance fee. how many games will kabir have to play at each arcade to spend the same amount of money at each arcade?

Explanation:

Step1: Define variable

Let \( x \) be the number of games Kabir plays.

Step2: Cost for first arcade

The cost for the first arcade is the entrance fee plus the cost per game times the number of games. So it is \( 5 + 0.75x \).

Step3: Cost for second arcade

The cost for the second arcade is just the cost per game times the number of games, which is \( 1.25x \).

Step4: Set costs equal

To find when the costs are the same, set the two expressions equal: \( 5 + 0.75x = 1.25x \).

Step5: Solve for x

Subtract \( 0.75x \) from both sides: \( 5 = 1.25x - 0.75x \), which simplifies to \( 5 = 0.5x \). Then divide both sides by \( 0.5 \): \( x=\frac{5}{0.5}=10 \).

Answer:

10