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. (1 point)

Question

Responses

74x+2,080=90x+1,760
; x=20
74 x plus 2,080 equals 90 x plus 1,760 ; x equals 20

2,080−74x=1,760−90x
; x=16
2,080 minus 74 x equals 1,760 minus 90 x ; x equals 16

74x+2,080=90x+1,760
; x=16
74 x plus 2,080 equals 90 x plus 1,760 ; x equals 16

2,080x+74=1,760x+90
; x=20

Answer 1

To find the number of days \( x \) it would take for the two movies to have the same number of views, we create an equation based on their view counts over time.

The first movie starts with 2,080 views and gains 74 views each day, which can be represented as: \[ 74x + 2080 \]

The second movie starts with 1,760 views and gains 90 views each day, which can be represented as: \[ 90x + 1760 \]

We set these two expressions equal to each other to find the value of \( x \):

\[ 74x + 2080 = 90x + 1760 \]

Now, let's solve for \( x \). First, rearrange the equation to get all terms involving \( x \) on one side and constant terms on the other:

\[ 2080 - 1760 = 90x - 74x \]

This simplifies to:

\[ 320 = 16x \]

Next, 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.

The correct response is:

74x + 2,080 = 90x + 1,760; x = 20.