1

Part of 2024 AIME

Problems(2)

the numbers sum to 2024

Source: 2024 AIME II Problem 1

900

residents of Aimeville, there are

195

who own a diamond ring,

367

who own a set of golf clubs, and

562

who own a garden spade. In addition, each of the

900

residents owns a bag of candy hearts. There are

437

residents who own exactly two of these things, and

234

residents who own exactly three of these things. Find the number of residents of Aimeville who own all four of these things.

Reread again and again and again and again…

Source: 2024 AIME I Problem 1

Every morning, Aya does a

9

kilometer walk, and then finishes at the coffee shop. One day, she walks at

s

kilometers per hour, and the walk takes

4

hours, including

t

minutes at the coffee shop. Another morning, she walks at

s+2

kilometers per hour, and the walk takes

2

24

minutes, including

t

minutes at the coffee shop. This morning, if she walks at

s+\frac12

kilometers per hour, how many minutes will the walk take, including the

t

minutes at the coffee shop?