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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineFarid received some gift cards for music and movie downloads for his birthday. Using one of them, he downloaded 1212 songs and 1818 movies, which cost a total of $186\$186. Using another, he purchased 1818 songs and 1515 movies, which cost a total of $171\$171. How much does each download cost?\newlineDownloads cost $_\$\_ for a song and $_\$\_ for a movie.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineFarid received some gift cards for music and movie downloads for his birthday. Using one of them, he downloaded 1212 songs and 1818 movies, which cost a total of $186\$186. Using another, he purchased 1818 songs and 1515 movies, which cost a total of $171\$171. How much does each download cost?\newlineDownloads cost $_\$\_ for a song and $_\$\_ for a movie.
  1. Define variables: Define variables for the cost of each type of download. Let ss be the cost of a song and mm be the cost of a movie. Farid's first card usage gives the equation 12s+18m=18612s + 18m = 186.
  2. Write second equation: Write the equation for the second card usage. Farid bought 1818 songs and 1515 movies for $171\$171, leading to the equation 18s+15m=17118s + 15m = 171.
  3. Use elimination method: Use elimination to solve the system. Multiply the first equation by 1515 and the second by 1818 to align the coefficients of mm. This results in 180s+270m=2790180s + 270m = 2790 and 324s+270m=3078324s + 270m = 3078.
  4. Subtract equations: Subtract the first new equation from the second to eliminate mm. This gives 144s=288144s = 288.
  5. Solve for ss: Solve for ss. Dividing both sides by 144144, we find s=2s = 2.
  6. Substitute and solve for mm: Substitute s=2s = 2 back into the first original equation to find mm. Plugging in, we get 12(2)+18m=18612(2) + 18m = 186, which simplifies to 24+18m=18624 + 18m = 186.
  7. Substitute and solve for mm: Substitute s=2s = 2 back into the first original equation to find mm. Plugging in, we get 12(2)+18m=18612(2) + 18m = 186, which simplifies to 24+18m=18624 + 18m = 186. Solve for mm. Subtract 2424 from both sides to get 18m=16218m = 162, then divide by 1818 to find m=9m = 9.

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