Angie and Kenny play online video games. Angie buys 1 software package and 1 month of game play. Kenny buys 1 software package and 3 month of game play. Each software package costs $35. If their total cost is $114, what is the cost of one month of game play?
The cost of one month of game play is $?
Let's assume the cost of one month of game play is x dollars.
Therefore, the cost of Angie's purchase would be 35 + x dollars.
And the cost of Kenny's purchase would be 35 + 3x dollars.
The total cost of their purchases is 114 dollars, so we can write the equation:
35 + x + 35 + 3x = 114
Combining like terms, we get:
4x + 70 = 114
Subtracting 70 from both sides of the equation, we get:
4x = 44
Dividing both sides by 4, we get:
x = 11
Therefore, the cost of one month of game play is $11.
A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $66. A season ski pass costs $450. The skier would have to rent skis with either pass for $30 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
The skier would have to go skiing
Let's assume the number of days the skier needs to go skiing is d.
For the daily pass, the skier would have to pay $66 per day for skiing and an additional $30 per day for renting skis. So, the total cost for each day with a daily pass would be $66 + $30 = $96.
For the season pass, the skier would have to pay $450 for the entire season, regardless of the number of days they go skiing. Additionally, they would have to pay $30 per day for renting skis.
To make the season pass less expensive than the daily passes, the skier would need to ensure that the total cost with the daily pass is greater than the cost with the season pass. Therefore, we can write the inequality:
96d > 450 + 30d
Subtracting 30d from both sides, we get:
66d > 450
Dividing both sides by 66, we get:
d > 450 / 66
d > 6.82 (rounded to two decimal places)
Since the number of days must be a whole number, the skier would have to go skiing for at least 7 days to make the season pass less expensive than the daily passes.
Solve the equation for y. Then find the value of y for each value of x.
y+2x=5;x=-2,0,4
Solve the equation for y.
To solve the equation for y, we'll substitute the given values of x into the equation one by one and solve for y.
Given equation: y + 2x = 5
For x = -2:
y + 2(-2) = 5
y - 4 = 5
Adding 4 to both sides:
y = 5 + 4
y = 9
For x = 0:
y + 2(0) = 5
y + 0 = 5
y = 5
For x = 4:
y + 2(4) = 5
y + 8 = 5
Subtracting 8 from both sides:
y = 5 - 8
y = -3
The values of y for x = -2, 0, and 4 are 9, 5, and -3, respectively.
When x,=0 the value of y is
enter your response here
Based on the equation y + 2x = 5, when x = 0, we can substitute 0 for x and solve for y:
y + 2(0) = 5
y + 0 = 5
y = 5
Therefore, when x = 0, the value of y is 5.
When x,=4 the value of y is
Based on the equation y + 2x = 5, when x = 4, we can substitute 4 for x and solve for y:
y + 2(4) = 5
y + 8 = 5
y = 5 - 8
y = -3
Therefore, when x = 4, the value of y is -3.
To find the cost of one month of game play, we need to set up a simple equation.
Let's assume the cost of one month of game play is "x" dollars.
According to the given information, Angie buys 1 software package and 1 month of game play, while Kenny buys 1 software package and 3 months of game play.
So, Angie's total cost is $35 (for the software package) + $x (for 1 month of game play).
Kenny's total cost is $35 (for the software package) + $3x (for 3 months of game play).
The total cost for both Angie and Kenny is $114.
So, we can set up the equation: $35 + $x + $35 + $3x = $114.
By simplifying the equation: $2x + $70 = $114.
We can then solve for x by subtracting $70 from both sides of the equation: $2x = $114 - $70.
Which gives us: $2x = $44.
Finally, divide both sides of the equation by 2 to solve for x: x = $44 / 2.
Therefore, the cost of one month of game play is $22.