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.(1 point)
Responses
10x=32−6x ; x=2
10 x equals 32 minus 6 x ; x equals 2
10x=32+6x ; x=8
10 x equals 32 plus 6 x ; x equals 8
10=32+6x ; x=−3
10 equals 32 plus 6 x ; x equals negative 3
10x=32+6x ; x=4
10 x equals 32 plus 6 x ; x equals 4
10x = 32 + 6x
10x - 6x = 32
4x = 32
x = 8
It would take 8 visits for the cost of the two plans to be equal.
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?(1 point)
Responses
After 8 weeks they will have the same amount of gas in their tanks.
After 8 weeks they will have the same amount of gas in their tanks.
After −8 weeks they will have the same amount of gas in their tanks.
After negative 8 weeks they will have the same amount of gas in their tanks.
After 18 week they will have the same amount of gas in their tanks.
After Start Fraction 1 over 8 End Fraction week they will have the same amount of gas in their tanks.
After 1.6 weeks they will have the same amount of gas in their tanks.
Miguel's rate of gas consumption: 1.5 gallons per week
Christina's rate of gas consumption: 1 gallon per week
The difference in gas consumption rate per week is 1.5 - 1 = 0.5 gallons.
To reach the same amount of gas in their tanks, they need to make up the difference of 0.5 gallons each week.
Capacity difference: 20 - 16 = 4 gallons
Number of weeks to reach 4 gallons at a rate of 0.5 gallons per week:
4 / 0.5 = 8 weeks
After 8 weeks, Miguel and Christina will have the same amount of gas in their tanks.
Therefore, the correct response is:
After 8 weeks they will have the same amount of gas in their tanks.
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 no solution.
The equation has no solution.
The equation has infinite solutions.
The equation has infinite solutions.
11x = 3(7x - 1) - 10x
11x = 21x - 3 - 10x
11x = 11x - 3
Since the variables cancel out when solving this equation, it results in a statement that says -3 = -3, which is always true.
Therefore, the equation has infinite solutions.
The correct response is:
The equation has infinite solutions.
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 one solution: x=1.
The equation has one solution: x equals 1 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has no solution.
Let's solve the equation:
5(2x + 2) - 4 = 2x + 6
10x + 10 - 4 = 2x + 6
10x + 6 = 2x + 6
10x - 2x = 6 - 6
8x = 0
x = 0
Therefore, the equation has one solution: x = 0.
The correct response is:
The equation has one solution: x = 0.
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.
Let's set up equations for both songs in terms of days:
For the first song: Listens = 700 + 52d, where d is the number of days.
For the second song: Listens = 600 + 56d
To find out when the two songs will have the same number of listens, we can set the two expressions equal to each other and solve for d:
700 + 52d = 600 + 56d
52d - 56d = 600 - 700
-4d = -100
d = 25
Therefore, the two songs will have the same number of listens after 25 days.