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? $\newline$ ◻

Full solution

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?

\newline

◻

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 $0.40$ : $T = \frac{32}{0.40}$ .
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 $0.75 \times 80$ 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 $0.75 \times 80$ toys.Calculating Harry's toys gives us: Harry had $60$ toys on Monday.