at the beginning of the month a video streaming service already has 2,130 views, and was getting 80 new views each day. Meanwhile, a video on a different service already had 1,800 views, and was getting 90 new views each day. Write an equation to show the number of days it would take for the two videos to have the same number of views. Use x as your variable.

Question

a. 80x + 2,130 = 90x +1,800
b. 80x + 1,800 = 90x + 2,130
c. 2,130 - 80x = 1,800 - 90x
d. 80x - 2,130 = 90x - 1,800

Answer 1

To find the number of days it would take for the two videos to have the same number of views, we can set up the following equations:

1. The first video starts with 2,130 views and gains 80 views per day, which can be expressed as: \[ \text{Views of Video 1} = 2130 + 80x \]

2. The second video starts with 1,800 views and gains 90 views per day, which can be expressed as: \[ \text{Views of Video 2} = 1800 + 90x \]

To find when the views of the two videos are equal, we can set the two expressions equal to each other: \[ 2130 + 80x = 1800 + 90x \]

Rearranging this equation leads us to: \[ 80x + 2130 = 90x + 1800 \]

This matches option a: \[ 80x + 2,130 = 90x + 1,800 \]

Thus, the correct answer is a.

Answer 2

a dance studio has two participation plans. For the first plan, the cost $20 per visit. For the second plan, the cost $45 per month, and $5 per visit. Write an equation to show the number of visits per month that it would take for the two plans to be equal. Use x as your variable.

a. 20x = 45 + 5x
b. 20x = 45x + 5
c. 5x = 20x + 45
d. 45x = 20 + 5x

Answer 3

To determine the number of visits per month (\(x\)) at which the costs of the two participation plans would be equal, we need to set up equations for both plans.

1. First Plan: The cost is $20 per visit, which can be expressed as: \[ \text{Cost of Plan 1} = 20x \]

2. Second Plan: The cost is $45 per month plus $5 per visit, which can be expressed as: \[ \text{Cost of Plan 2} = 45 + 5x \]

To find out when the costs of the two plans are equal, we can set these two equations equal to each other: \[ 20x = 45 + 5x \]

This matches option a: \[ 20x = 45 + 5x \]

Thus, the correct answer is a.