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?◻
Q. 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?◻
Define Variables: Let's call the number of toys Teddy had on Monday "T". Harry had 75% as many toys as Teddy, so Harry had 0.75T toys on Monday.
Calculate Harry's Toys on Tuesday: On Tuesday, Harry gets 32 more toys, so he has 0.75T+32 toys now.
Calculate Teddy's Toys on Tuesday: Teddy gets 15% more toys on Tuesday. 15% of T is 0.15T, so Teddy has T+0.15T=1.15T toys now.
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=1.15T.
Solve for T: To solve for T, we'll subtract 0.75T from both sides: 32=1.15T−0.75T.
Simplify Equation: Now we simplify the right side: 32=0.40T.
Find T: To find T, we divide both sides by 0.40: T=0.4032.
Calculate Teddy's Toys on Monday: Calculating T gives us: T=80. So Teddy had 80 toys on Monday.
Calculate Harry's Toys on Monday: Now we need to find out how many toys Harry had on Monday. We know Harry had 0.75T toys, so Harry had 0.75×80 toys.
Calculate Harry's Toys on Monday: Now we need to find out how many toys Harry had on Monday. We know Harry had 0.75T toys, so Harry had 0.75×80 toys.Calculating Harry's toys gives us: Harry had 60 toys on Monday.
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