At the beginning of the month, a movie on a streaming service had 2,080 views, and it was getting 74 new views each day. Meanwhile, a different movie had 1,760 views, and it was getting 90 new views each day. Write and solve an equation to show the number of days it would take for the two videos to have the same number of views.

Answer 1

To find out how many days it will take for the two movies to have the same number of views, we can set up equations based on the information given.

Let \( x \) represent the number of days after the beginning of the month.

For the first movie:

• Initial views: 2,080
• Daily views increase: 74
• Total views after \( x \) days: \[ V_1 = 2080 + 74x \]

For the second movie:

• Initial views: 1,760
• Daily views increase: 90
• Total views after \( x \) days: \[ V_2 = 1760 + 90x \]

To find when both movies will have the same number of views, we set the two equations equal to each other: \[ 2080 + 74x = 1760 + 90x \]

Next, we will solve for \( x \):

1. Subtract \( 74x \) from both sides: \[ 2080 = 1760 + 90x - 74x \] \[ 2080 = 1760 + 16x \]

2. Subtract 1760 from both sides: \[ 2080 - 1760 = 16x \] \[ 320 = 16x \]

3. Divide both sides by 16: \[ x = \frac{320}{16} = 20 \]

Thus, it will take 20 days for the two movies to have the same number of views.

To verify, we can calculate the views after 20 days:

• Views for the first movie: \[ V_1 = 2080 + 74 \times 20 = 2080 + 1480 = 3560 \]

• Views for the second movie: \[ V_2 = 1760 + 90 \times 20 = 1760 + 1800 = 3560 \]

Both movies will have 3,560 views after 20 days, confirming our solution is correct. The answer is:

20 days.