Angie and Kenny play online video games. Angie buys 1 software and 2 monhs of game play. Kenny buys 2 software and 5 months of game play. Each software package costs $40. If their total cost is $253, what is the cost of one month of game play?
Let's assume the cost of one month of gameplay is x.
Angie's total cost is 1 * $40 (cost of software) + 2 * x (cost of 2 months of gameplay) = $40 + 2x.
Kenny's total cost is 2 * $40 (cost of software) + 5 * x (cost of 5 months of gameplay) = $80 + 5x.
The total cost for Angie and Kenny is: $40 + 2x + $80 + 5x = $120 + 7x.
Since their total cost is $253, we can solve the equation: $120 + 7x = $253.
Subtracting $120 from both sides, we get: 7x = $133.
Dividing both sides by 7, we get: x = $19.
So, the cost of one month of gameplay is $19. Answer: \boxed{19}.
Let's break down the information given and solve the problem step-by-step:
Let's say the cost of one month of gameplay is x dollars.
Angie buys 1 software package and 2 months of gameplay, which cost $40 + 2x dollars in total.
Kenny buys 2 software packages and 5 months of gameplay, which cost 2 * $40 + 5x dollars in total.
The total cost of their purchases is $253.
So, we can set up the equation:
(1 software cost + 2 months cost) + (2 software cost + 5 months cost) = $253
Simplifying the equation, we have:
$40 + 2x + $80 + 5x = $253
Combining like terms, we have:
$120 + 7x = $253
To isolate the variable x, we subtract $120 from both sides of the equation:
7x = $253 - $120
Simplifying, we have:
7x = $133
To solve for x, we divide both sides of the equation by 7:
x = $133 / 7
Therefore, the cost of one month of gameplay is approximately $19.
To solve this problem, we need to set up a system of equations representing the given information. Let's use the variables x and y to represent the costs of one software package and one month of gameplay, respectively.
According to the problem, Angie buys 1 software and 2 months of gameplay, which gives us the equation:
1x + 2y = total cost for Angie
Similarly, Kenny buys 2 software packages and 5 months of gameplay, which gives us the equation:
2x + 5y = total cost for Kenny
We know that each software package costs $40, so we can substitute this value for x in both equations:
1(40) + 2y = total cost for Angie
2(40) + 5y = total cost for Kenny
Simplifying these equations gives us:
40 + 2y = total cost for Angie
80 + 5y = total cost for Kenny
Since the total cost for both Angie and Kenny combined is $253, we can combine the two equations:
40 + 2y + 80 + 5y = 253
Combine like terms:
120 + 7y = 253
Subtract 120 from both sides of the equation:
7y = 253 - 120
7y = 133
Divide both sides of the equation by 7 to solve for y:
y = 133/7
y = 19
Therefore, the cost of one month of gameplay is $19.