Question

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)
Responses

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

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

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

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

Answer 1

To solve for the number of days until the two movies have the same number of views, we start by setting up the equation based on the information provided.

Let \( x \) be the number of days.

The first movie's views after \( x \) days would be:
\[
2,080 + 74x
\]

The second movie's views after \( x \) days would be:
\[
1,760 + 90x
\]

We want to find \( x \) such that the views are equal:
\[
2,080 + 74x = 1,760 + 90x
\]

Now, let's solve this equation step by step:

1. **Rearranging the equation**:
\[
2,080 - 1,760 = 90x - 74x
\]
Simplifying this gives:
\[
320 = 16x
\]

2. **Solving for \( x \)**:
Divide both sides by 16:
\[
x = \frac{320}{16}
\]
\[
x = 20
\]

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

To verify:
- In 20 days, the first movie would have:
\[
2,080 + 74(20) = 2,080 + 1,480 = 3,560
\]
- The second movie would have:
\[
1,760 + 90(20) = 1,760 + 1,800 = 3,560
\]

Both calculations show that after 20 days, both movies will indeed have the same number of views (3,560).

So, the correct equation was:
\[
74x + 2,080 = 90x + 1,760
\]
And the solution \( x = 20 \) is accurate.