Tracy had a bag of candies, and none of the candies could be broken into pieces. She ate $\frac{1}{3}$ of them and then gave $\frac{1}{4}$ of what remained to her friend Rachel. Tracy and her mom then each ate 15 candies from what Tracy had left. Finally, Tracy's brother took somewhere from one to five candies, leaving Tracy with three candies. How many candies did Tracy have at the start?

72

Step-by-step explanation:

Let x be Tracy's starting number of candies. After eating of them, she had left. Since is an integer, x is divisible by 3. After giving of this to Rachel, she had of left, for a total of . Since is an integer, x is divisible by 2. Since x is divisible by both 2 and 3, it is divisible by 6.

After Tracy and her mom each ate 15 candies (they ate a total of 30), Tracy had candies left. After her brother took between 1 and 5 candies, Tracy was left with 3. This means Tracy had between 4 and 8 candies before her brother took some candies. Hence,

Since x is divisible by 6, and the only multiple of 6 in the above range is 72, we have x = .

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol