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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineShawn and Gary each want to run for president of their school's student body council. In order to do so, they must collect a certain number of signatures and get a nomination. So far, Shawn has 2525 signatures, and Gary has 2020. Shawn is collecting signatures at an average rate of 88 per day, whereas Gary is averaging 99 signatures every day. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. How long will that take? How many signatures will they both have?\newlineIn _\_ days, Shawn and Gary will each have collected _\_ signatures.

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineShawn and Gary each want to run for president of their school's student body council. In order to do so, they must collect a certain number of signatures and get a nomination. So far, Shawn has 2525 signatures, and Gary has 2020. Shawn is collecting signatures at an average rate of 88 per day, whereas Gary is averaging 99 signatures every day. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. How long will that take? How many signatures will they both have?\newlineIn _\_ days, Shawn and Gary will each have collected _\_ signatures.
  1. Define variables: Let's define the variables. Let xx be the number of days after which Shawn and Gary will have the same number of signatures. Shawn starts with 2525 signatures and collects 88 per day. Gary starts with 2020 signatures and collects 99 per day.\newlineShawn's total signatures after xx days: 25+8x25 + 8x\newlineGary's total signatures after xx days: 20+9x20 + 9x
  2. Set up equation: Set up the equation where Shawn's and Gary's total signatures are equal. 25+8x=20+9x25 + 8x = 20 + 9x
  3. Solve for x: Solve for x by rearranging the equation.\newline25−20=9x−8x25 - 20 = 9x - 8x\newline5=x5 = x
  4. Calculate total signatures: Calculate the total number of signatures each will have after xx days.\newlineShawn's total signatures: 25+8(5)=25+40=6525 + 8(5) = 25 + 40 = 65\newlineGary's total signatures: 20+9(5)=20+45=6520 + 9(5) = 20 + 45 = 65

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