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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineLuca wrote a business plan for an entrepreneurship class, and now he has to make bound copies. Luca could use a printer who charges a setup fee of $38\$38 and $5\$5 for every copy printed. Another possibility is to go to the office supply store, where he could pay an up-front fee of $34\$34 and $9\$9 per copy. There is a certain number of copies that makes the two options equivalent in terms of cost. How much would the copies cost? How many copies is that?\newlineThe cost is $____\$\_\_\_\_ for ____\_\_\_\_ copies.

Full solution

Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineLuca wrote a business plan for an entrepreneurship class, and now he has to make bound copies. Luca could use a printer who charges a setup fee of $38\$38 and $5\$5 for every copy printed. Another possibility is to go to the office supply store, where he could pay an up-front fee of $34\$34 and $9\$9 per copy. There is a certain number of copies that makes the two options equivalent in terms of cost. How much would the copies cost? How many copies is that?\newlineThe cost is $____\$\_\_\_\_ for ____\_\_\_\_ copies.
  1. Set up equations: Step 11: Set up equations for both printing options.\newlineLuca's cost using the first printer: Cost = $38\$38 + $5\$5 per copy.\newlineLet xx be the number of copies, then the equation is C=5x+38C = 5x + 38.\newlineLuca's cost using the office supply store: Cost = $34\$34 + $9\$9 per copy.\newlineThe equation is C=9x+34C = 9x + 34.
  2. Equate equations: Step 22: Equate the two equations to find the number of copies where the costs are the same. 5x+38=9x+345x + 38 = 9x + 34
  3. Solve for x: Step 33: Solve for x.\newline5x9x=34385x - 9x = 34 - 38\newline4x=4-4x = -4\newlinex=1x = 1

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