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On Monday, Harry had 75% as many toys as Teddy did. On Tuesday, Harry acquires 32 more toys, and Teddy acquires 15% as many toys as he had on Monday. If Harry and Teddy now have the same number of toys, how many toys did Harry have on Monday?

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On Monday, Harry had 75%75\% as many toys as Teddy did. On Tuesday, Harry acquires 3232 more toys, and Teddy acquires 15%15\% as many toys as he had on Monday. If Harry and Teddy now have the same number of toys, how many toys did Harry have on Monday?\newline

Full solution

Q. On Monday, Harry had 75%75\% as many toys as Teddy did. On Tuesday, Harry acquires 3232 more toys, and Teddy acquires 15%15\% as many toys as he had on Monday. If Harry and Teddy now have the same number of toys, how many toys did Harry have on Monday?\newline
  1. Define Variables: Let's call the number of toys Teddy had on Monday "TT". Harry had 75%75\% as many toys as Teddy, so Harry had 0.75T0.75T toys on Monday.
  2. Calculate Harry's Toys on Tuesday: On Tuesday, Harry gets 3232 more toys, so he has 0.75T+320.75T + 32 toys now.
  3. Calculate Teddy's Toys on Tuesday: Teddy gets 15%15\% more toys on Tuesday. 15%15\% of TT is 0.15T0.15T, so Teddy has T+0.15T=1.15TT + 0.15T = 1.15T toys now.
  4. Set Up Equation: Since Harry and Teddy have the same number of toys now, we can set their toy counts equal to each other: 0.75T+32=1.15T0.75T + 32 = 1.15T.
  5. Solve for T: To solve for T, we'll subtract 0.75T0.75T from both sides: 32=1.15T0.75T32 = 1.15T - 0.75T.
  6. Simplify Equation: Now we simplify the right side: 32=0.40T32 = 0.40T.
  7. Find TT: To find TT, we divide both sides by 0.400.40: T=320.40T = \frac{32}{0.40}.
  8. Calculate Teddy's Toys on Monday: Calculating TT gives us: T=80T = 80. So Teddy had 8080 toys on Monday.
  9. Calculate Harry's Toys on Monday: Now we need to find out how many toys Harry had on Monday. We know Harry had 0.75T0.75T toys, so Harry had 0.75×800.75 \times 80 toys.
  10. Calculate Harry's Toys on Monday: Now we need to find out how many toys Harry had on Monday. We know Harry had 0.75T0.75T toys, so Harry had 0.75×800.75 \times 80 toys.Calculating Harry's toys gives us: Harry had 6060 toys on Monday.