At the beginning of the month, a song on a streaming service already had 1,000 listens, and was getting 38 new listens each day. Meanwhile, a different song already had 900 listens, and was getting 40 new listens each day. Write an equation to show the number of days it would take for the two songs to have the same number of listens. Use x as your variable.
Let's assume that the number of days it would take for the two songs to have the same number of listens is denoted by x.
For the first song, the number of listens after x days would be calculated as: 1,000 + 38x.
For the second song, the number of listens after x days would be calculated as: 900 + 40x.
To find the days it would take for the two songs to have the same number of listens, we need to set the equations equal to each other:
1,000 + 38x = 900 + 40x.
This equation represents the situation when both songs have the same number of listens. By solving this equation for x, we can find the number of days it would take for the two songs to have the same number of listens.
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.
10x=32−6x ; x=2
10x=32+6x ; x=4
10=32+6x ; x=−3
10x=32+6x ; x=8
To find the number of visits it would take for the cost of the two plans to be equal, we need to set the equations equal to each other.
Let's assume that x represents the number of visits.
Option 1: The cost of the first option is $10 per visit, so the total cost for x visits would be 10x.
Option 2: The cost of the second option is $32 per month plus $6 per visit. So the total cost for x visits would be 32 + 6x.
To find the number of visits for which the costs are equal, we set the equations equal to each other:
10x = 32 + 6x
Now, we solve this equation for x:
10x - 6x = 32
4x = 32
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?
Let's assume that the number of days it would take for the two songs to have the same number of listens is denoted by x.
For the first song, the number of listens after x days would be calculated as: 700 + 52x.
For the second song, the number of listens after x days would be calculated as: 600 + 56x.
To find when the two songs will have the same number of listens, we need to set the equations equal to each other:
700 + 52x = 600 + 56x.
Now, we solve this equation for x:
52x - 56x = 600 - 700
-4x = -100
x = 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?
After 1.6 weeks they will have the same amount of gas in their tanks.
After 1/8 week 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.
To find when Miguel and Christina will have the same amount of gas in their tanks, we need to compare the amount of gas consumed by both cars over time.
Let's assume that x represents the number of weeks.
Miguel's car will have 20 - 1.5x gallons of gas remaining after x weeks.
Christina's car will have 16 - 1x gallons of gas remaining after x weeks.
To find when they will have the same amount of gas, we need to set the equations equal to each other:
20 - 1.5x = 16 - x.
Now, we solve this equation for x:
-1.5x + x = 16 - 20
-0.5x = -4
x = 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?
−3x+8=−3x−8
−8x+3=−8x+3
3x−8=3x+8
−3x−8=3x−8
The equation that has exactly one solution is:
−3x + 8 = −3x - 8.
Solve for x to determine if the equation has one, none, or infinite solutions.
11x=3(7x−1)−10x
The equation has one solution: x=−1.
The equation has no solution.
The equation has infinite solutions.
The equation has one solution: x=−3.