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 8. On her second turn, she rolled 3 times her previous roll, but her friend played a card that decreased the number of spaces she moved by 4. In the end, she moved the same number of spaces on both turns.Which equation can you use to find r, the number Emma rolled on her first turn?Choices:(A) r+8=3r−4(B) r+8=3r+4What number did Emma roll on her first turn?____
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 8. On her second turn, she rolled 3 times her previous roll, but her friend played a card that decreased the number of spaces she moved by 4. In the end, she moved the same number of spaces on both turns.Which equation can you use to find r, the number Emma rolled on her first turn?Choices:(A) r+8=3r−4(B) r+8=3r+4What number did Emma roll on her first turn?____
Denote first roll as r: Let's denote the number Emma rolled on her first turn as r. According to the problem, she moved r+8 spaces on her first turn. On her second turn, she rolled 3 times her previous roll and then moved 3r−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=3r−4.
Set up equation: Now we need to solve the equation r+8=3r−4 for r. First, we will subtract r from both sides to get all the r terms on one side.8=2r−4
Solve for r: Next, we will add 4 to both sides to isolate the terms with r.8+4=2r12=2r
Final result: Finally, we will divide both sides by 2 to solve for r. 212=r6=r
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