Respuesta :
Answer:
72
Step-by-step explanation:
Let the number of candies = n
Tracy ate = 1/3 of n = n/3 remaining 2n / 3
she gave 1/4 of the remainder to her friend = 1/4 of ( n - n/3) = 2n / 12
the new remainder = (2n / 3) - (2n / 12) = n /2
she and her mom then ate altogether = 30
and the brother took from 1 to five, the number he took = x
and she has 3 left
( n/2) - 30 - x = 3
n = 2 ( 33 + x)
now we know that the candies could not be broken and x is between 1 to 5
n = 2 (33 + 1), 2 (33+2), 2(33 +3), 2 (33+ 4) and 2 (33 + 5) this are the possible values of n, ( 68, 70, 72, 74, 76) and the multiple of 3 is 72
n therefore = 72
Answer:
72
Step-by-step explanation:
Let x be Tracy's starting number of candies. After eating [tex]$\frac{1}{3}$[/tex] of them, she had [tex]$\frac{2}{3}x$[/tex] left. Since [tex]$\frac{2}{3}x$[/tex] is an integer, x is divisible by 3. After giving [tex]$\frac{1}{4}$[/tex] of this to Rachel, she had [tex]$\frac{3}{4}$[/tex] of [tex]$\frac{2}{3}x$[/tex] left, for a total of [tex]$\frac{3}{4} \cdot \frac{2}{3}x = \frac{1}{2}x$[/tex]. Since [tex]$\frac{1}{2}x$[/tex] 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 [tex]$\frac{1}{2}x - 30$[/tex] 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,
[tex]4 \le \frac{1}{2}x - 30 \le 8\qquad \Rightarrow \qquad 34 \le \frac{1}{2}x \le 38\qquad \Rightarrow \qquad 68 \le x \le 76.[/tex]
Since x is divisible by 6, and the only multiple of 6 in the above range is 72, we have x = [tex]\boxed{72}[/tex].
