An ice skating rink has two ways you can use the facility. The first option is to pay $10 per visit. The second option is to pay $32 per month, and $6 per visit. Write and solve an equation to show the number of visits it would take for the cost of the two plans to be equal
Let's assume the number of visits to the ice skating rink is 'x'.
For the first option, where the cost is $10 per visit, the equation would be:
$10x = total cost
For the second option, where the cost is $32 per month and $6 per visit, the equation would be:
$32 + $6x = total cost
To find the number of visits where the cost of both options is equal, we need to solve the equation:
$10x = $32 + $6x
Subtracting $6x from both sides of the equation:
$4x = $32
Dividing both sides by $4:
x = $32 / $4
Simplifying, we find:
x = 8
Therefore, it would take 8 visits for the cost of the two plans to be equal.
At the beginning of the month, a song on a streaming service had 700 listens, and it was getting 52 new listens each day. Meanwhile, a different song had 600 listens, and it was getting 56 new listens each day. When will the two songs have the same number of listens?(1 point)
The songs will have the same number of listens after __ days
To solve this problem, we need to find the number of days it takes for the total number of listens for both songs to be equal.
Let's represent the number of days as 'd'.
For the first song, the number of listens after 'd' days can be calculated using the equation:
Total listens for first song = 700 + 52d
For the second song, the number of listens after 'd' days can be calculated using the equation:
Total listens for second song = 600 + 56d
To find the number of days when the two songs have the same number of listens, we need to set the two equations equal to each other and solve for 'd':
700 + 52d = 600 + 56d
Subtracting 600 from both sides of the equation:
100 + 52d = 56d
Subtracting 52d from both sides of the equation:
100 = 4d
Dividing both sides by 4:
d = 25
Therefore, the two songs will have the same number of listens after 25 days.
Miguel’s car has a 20-gallon capacity, and Christina’s car has a 16-gallon capacity. Miguel uses 1.5 gallons of gas per week, and Christina uses 1 gallon of gas per week. When will Miguel and Christina have the same amount of gas in their tanks?
To find when Miguel and Christina will have the same amount of gas in their tanks, we need to determine after how many weeks their gas consumption will result in equal amounts.
Let's represent the number of weeks as 'w'.
For Miguel's car, the amount of gas remaining after 'w' weeks can be calculated using the equation:
Gas remaining in Miguel's car = 20 - 1.5w
For Christina's car, the amount of gas remaining after 'w' weeks can be calculated using the equation:
Gas remaining in Christina's car = 16 - 1w
To find when their gas amounts will be equal, we set the two equations equal to each other and solve for 'w':
20 - 1.5w = 16 - 1w
Subtracting 16 from both sides:
4 - 1.5w = -1w
Adding 1.5w to both sides:
4 = 0.5w
Dividing both sides by 0.5:
w = 8
Therefore, Miguel and Christina will have the same amount of gas in their tanks after 8 weeks.
Which of the following equations has exactly one solution?(1 point)
Responses
−3x+8=−3x−8
negative 3 x plus 8 equals negative 3 x minus 8
−3x−8=3x−8
negative 3 x minus 8 equals 3 x minus 8
3x−8=3x+8
3 x minus 8 equals 3 x plus 8
−8x+3=−8x+3
The equation that has exactly one solution is:
−8x+3=−8x+3
Solve for x to determine if the equation has one, none, or infinite solutions.
11x=3(7x−1)−10x(1 point)
Responses
The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .
The equation has one solution: x=−1.
The equation has one solution: x equals negative 1 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has no solution.
To determine the solution for the equation 11x = 3(7x-1) - 10x, we can simplify and solve for x:
Expanding the right side of the equation:
11x = 21x - 3 - 10x
Combining like terms:
11x = 11x - 3
Subtracting 11x from both sides:
0 = -3
This equation results in 0 = -3, which is not a true statement. Therefore, there are no solutions for this equation, and the correct response is:
The equation has no solution.
Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−4=2x+6(1 point)
Responses
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has no solution.
The equation has no solution.
The equation has one solution: x=1.
The equation has one solution: x equals 1 .
The equation has infinite solutions.