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=2
10 x equals 32 minus 6 x ; x equals 2
10x=32+6x ; x=4
10x=32+6x ; x=4
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 say the number of days it takes for the two songs to have the same number of listens is represented by "d".
For the first song:
Number of listens = 700 + 52d
For the second song:
Number of listens = 600 + 56d
To find when the two songs will have the same number of listens, we can set the two equations equal to each other and solve for "d":
700 + 52d = 600 + 56d
Rearranging the equation:
52d - 56d = 600 - 700
-4d = -100
Dividing by -4 on both sides of the equation:
d = -100 / -4
d = 25
So, the two songs will have the same number of listens after 25 days.
10x = 32 + 6x is the correct equation to represent the cost of the two plans being equal. Now, we can solve for x.
Subtract 6x from both sides of the equation:
10x - 6x = 32
Combine like terms:
4x = 32
Divide both sides of the equation by 4:
x = 8
Therefore, it would take 8 visits for the cost of the two plans to be equal.