At the beginning of the month, a song on a streaming service already had 1,000 listens, and was getting 38 new listens each day. Meanwhile, a different song already had 900 listens, and was getting 40 new listens each day. Write an equation to show the number of days it would take for the two songs to have the same number of listens. Use x as your variable.(2 points)

Question

At the beginning of the month, a song on a streaming service already had 1,000 listens, and was getting 38 new listens each day. Meanwhile, a different song already had 900 listens, and was getting 40 new listens each day. Write an equation to show the number of days it would take for the two songs to have the same number of listens. Use x as your variable.(2 points)
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GPT-4o mini · Answer

To find the number of days $ x $ it would take for the two songs to have the same number of listens, we can set up equations that represent the total listens for each song. For the first song: - Initial listens: 1,000 - New listens per day: 38 - Total listens after $ x $ days: $ 1000 + 38x $ For the second song: - Initial listens: 900 - New listens per day: 40 - Total listens after $ x $ days: $ 900 + 40x $ To find when the two songs have the same number of listens, we can set their total listens equal to each other: $$ 1000 + 38x = 900 + 40x $$ Now, we can solve for $ x $: 1. Subtract $ 38x $ from both sides: $$ 1000 = 900 + 2x $$ 2. Subtract 900 from both sides: $$ 1000 - 900 = 2x $$ $$ 100 = 2x $$ 3. Divide both sides by 2: $$ x = 50 $$ Thus, the equation representing the number of days until the listens are equal is: $$ x = 50 $$