Question

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

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=8
10 x equals 32 plus 6 x ; x equals 8

Answer 1

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)

Answer 2

10x = 32 + 6x

Subtract 6x from both sides:

4x = 32

Divide by 4:

x = 8

It would take 8 visits for the cost of the two plans to be equal.

Answer 3

Let x be the number of days it takes for the two songs to have the same number of listens.

For the first song:
Total listens = 700 + 52x

For the second song:
Total listens = 600 + 56x

We want these two quantities to be equal:

700 + 52x = 600 + 56x

Subtract 600 from both sides:

100 + 52x = 56x

Subtract 52x from both sides:

100 = 4x

Divide by 4:

x = 25

It will take 25 days for the two songs to have the same number of listens.