Question:
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.
Answer Choices
* 50
* x = 50
Equation: 1000 + 38x = 900 + 40x
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 L1 represent the total listens for the first song and L2 represent the total listens for the second song.
For the first song, the total listens can be calculated as L1 = 1000 + 38x.
For the second song, the total listens can be calculated as L2 = 900 + 40x.
To find when the two songs will have the same number of listens, set L1 equal to L2:
1000 + 38x = 900 + 40x
Therefore, the equation representing the number of days it would take for the two songs to have the same number of listens is:
1000 + 38x = 900 + 40x
Simplifying this equation leads to:
1000 - 900 = 40x - 38x
100 = 2x
2x = 100
x = 50
Therefore, it would take 50 days for the two songs to have the same number of listens. Hence, the correct answer is:
x = 50
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=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 ; x=2
10x = 32 + 6x
Subtract 6x from both sides:
10x - 6x = 32
4x = 32
Divide by 4 on both sides to solve for x:
x = 32 / 4
x = 8
Therefore, the correct answer is:
10x = 32 + 6x ; x = 8
Or in words:
10 times the number of visits is equal to $32 plus 6 times the number of visits, which means 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.
Let L1 represent the total listens for the first song and L2 represent the total listens for the second song.
For the first song, the total listens can be calculated as L1 = 700 + 52x, where x represents the number of days.
For the second song, the total listens can be calculated as L2 = 600 + 56x, where x represents the number of days.
To find when the two songs will have the same number of listens, set L1 equal to L2:
700 + 52x = 600 + 56x
Therefore, the equation representing the number of days it would take for the two songs to have the same number of listens is:
700 + 52x = 600 + 56x
Simplifying this equation leads to:
700 - 600 = 56x - 52x
100 = 4x
4x = 100
x = 25
Therefore, the songs will have the same number of listens after 25 days.
Which of the following equations has exactly one solution?(1 point)
Responses
−8x+3=−8x+3
negative 8 x plus 3 equals negative 8 x plus 3
3x−8=3x+8
3 x minus 8 equals 3 x plus 8
−3x−8=3x−8
negative 3 x minus 8 equals 3 x minus 8
−3x+8=−3x−8
To have exactly one solution, the equation must be such that when you simplify it, x should not cancel out or disappear. There must be a unique value for x.
The equation that has exactly one solution is:
3x - 8 = 3x + 8
Explanation:
Subtracting 3x from both sides gives:
-8 = 8
This leads to a contradiction which means that the equation 3x - 8 = 3x + 8 has no solution and that's what makes it have exactly one solution.
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 infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .
The equation has no solution.
The equation has no solution.
The equation has one solution: x=−1.