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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineReggie and his good buddy Isaiah are both mechanics at a shop that does oil changes. They are in a friendly competition to see who can complete the most oil changes in one day. Reggie has already finished 55 oil changes today, and can complete more at a rate of 33 oil changes per hour. Isaiah just came on shift, and can finish 44 oil changes every hour. Sometime during the day, the friends will be tied, with the same number of oil changes completed. How long will that take? How many oil changes will Reggie and Isaiah each have done?\newlineIn _\_ hours, both men will have completed _\_ oil changes.

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineReggie and his good buddy Isaiah are both mechanics at a shop that does oil changes. They are in a friendly competition to see who can complete the most oil changes in one day. Reggie has already finished 55 oil changes today, and can complete more at a rate of 33 oil changes per hour. Isaiah just came on shift, and can finish 44 oil changes every hour. Sometime during the day, the friends will be tied, with the same number of oil changes completed. How long will that take? How many oil changes will Reggie and Isaiah each have done?\newlineIn _\_ hours, both men will have completed _\_ oil changes.
  1. Define Variables: Let xx represent the hours passed since Isaiah started working, and yy represent the total oil changes completed by each. For Reggie: Starting oil changes = 55, Rate = 33 oil changes per hour. Equation: y=3x+5y = 3x + 5
  2. Reggie's Equation: For Isaiah: Starting oil changes = 00 (just started), Rate = 44 oil changes per hour. Equation: y=4xy = 4x
  3. Isaiah's Equation: Set the equations equal to find when they have completed the same number of oil changes: 3x+5=4x3x + 5 = 4x
  4. Set Equations Equal: Solve for xx: Subtract 3x3x from both sides: 5=x5 = x

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