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Emma and her friends played a board game that uses cards and dice to determine how many spaces they move. On her first turn, Emma rolled the dice and then played a card that increased the number of spaces she moved by 88. On her second turn, she rolled 33 times her previous roll, but her friend played a card that decreased the number of spaces she moved by 44. In the end, she moved the same number of spaces on both turns.\newlineWhich equation can you use to find rr, the number Emma rolled on her first turn?\newlineChoices:\newline(A) r+8=3r4r + 8 = 3r - 4\newline(B) r+8=3r+4r + 8 = 3r + 4\newlineWhat number did Emma roll on her first turn?\newline____

Full solution

Q. Emma and her friends played a board game that uses cards and dice to determine how many spaces they move. On her first turn, Emma rolled the dice and then played a card that increased the number of spaces she moved by 88. On her second turn, she rolled 33 times her previous roll, but her friend played a card that decreased the number of spaces she moved by 44. In the end, she moved the same number of spaces on both turns.\newlineWhich equation can you use to find rr, the number Emma rolled on her first turn?\newlineChoices:\newline(A) r+8=3r4r + 8 = 3r - 4\newline(B) r+8=3r+4r + 8 = 3r + 4\newlineWhat number did Emma roll on her first turn?\newline____
  1. Denote first roll as rr: Let's denote the number Emma rolled on her first turn as rr. According to the problem, she moved r+8r + 8 spaces on her first turn. On her second turn, she rolled 33 times her previous roll and then moved 3r43r - 4 spaces after her friend played a card. Since she moved the same number of spaces on both turns, we can set up the equation r+8=3r4r + 8 = 3r - 4.
  2. Set up equation: Now we need to solve the equation r+8=3r4r + 8 = 3r - 4 for rr. First, we will subtract rr from both sides to get all the rr terms on one side.\newline8=2r48 = 2r - 4
  3. Solve for rr: Next, we will add 44 to both sides to isolate the terms with rr.\newline8+4=2r8 + 4 = 2r\newline12=2r12 = 2r
  4. Final result: Finally, we will divide both sides by 22 to solve for rr. \newline122=r\frac{12}{2} = r\newline6=r6 = r

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