Final answer:
To find the number of games played at Amanda's Bowling Lanes, set up a linear equation based on the costs at both alleys, assuming you spent the same total amount at each. You solve for the number of games by choosing a whole number of games played at Dexter's Bowling Alley and substituting that into the simplified equation to find a corresponding positive whole number of games at Amanda's that matches one of the provided options.
Step-by-step explanation:
The question involves solving a system of linear equations to find out the number of games played at Amanda's Bowling Lanes when the same amount of money is spent at both bowling alleys. To find the solution, we first need to set up the equations based on the provided information:
Let x be the number of games played at Dexter's Bowling Alley and y be the number of games played at Amanda's Bowling Lanes. The total cost at Dexter's is the shoe rental fee plus the cost per game multiplied by the number of games: 2.50 + 0.45x. Similarly, the total cost at Amanda's is the shoe rental fee plus the cost per game multiplied by the number of games: 7.50 + 0.25y.
Since the total amount spent at both alleys is the same, we set the two expressions equal to each other:
- 2.50 + 0.45x = 7.50 + 0.25y
By rearranging the terms, we isolate y:
- 0.25y = 0.45x + 2.50 - 7.50
- 0.25y = 0.45x - 5
Now, multiply everything by 4 to get rid of the decimal and to simplify the equation:
The number of games played at Dexter's (x) has to be a whole number because you can't play a fraction of a game. Let's assume you played 10 games (though this number is not directly provided, it's for illustration purposes); the equation would be:
- y = 1.8(10) - 20
- y = 18 - 20
- y = -2
Since the number of games played cannot be negative, another value for x must be chosen. You continue testing whole number values for x until you find a positive whole number value for y that matches one of the multiple-choice answers given (A. 28 games, B. 25 games, C. 22 games, D. 30 games).