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Abby and Raju had the same number of marbles at First. After Raju bought another 3737 marbles and Abby gave 6565 marbles away, they has a total of 284284 marbles together left. How much marbles each of them have at First?

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Full solution

Q. Abby and Raju had the same number of marbles at First. After Raju bought another 3737 marbles and Abby gave 6565 marbles away, they has a total of 284284 marbles together left. How much marbles each of them have at First?
  1. Initial Marbles: Abby and Raju started with the same number of marbles, let's call this number xx. So, Abby had xx marbles and Raju also had xx marbles.
  2. Raju's Purchase: Raju bought 3737 more marbles, so he then had x+37x + 37 marbles.
  3. Abby's Giveaway: Abby gave away 6565 marbles, so she then had x−65x - 65 marbles.
  4. Total Marbles Equation: Together, they had a total of 284284 marbles left after the transactions. So, we can write the equation: (x+37)+(x−65)=284(x + 37) + (x - 65) = 284.
  5. Solving the Equation: Now, let's solve the equation: 2x−28=2842x - 28 = 284 (since x+x=2xx + x = 2x and 37−65=−2837 - 65 = -28).
  6. Isolating xx: Add 2828 to both sides of the equation to isolate the term with xx: 2x=284+282x = 284 + 28.
  7. Calculating Sum: Calculate the sum: 2x=3122x = 312.
  8. Dividing by 22: Divide both sides by 22 to find the value of x: x=3122x = \frac{312}{2}.
  9. Final Marbles Count: Calculate the division: x=156x = 156. So, Abby and Raju each had 156156 marbles at first.

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