Respuesta :
Answer:
The number of candies in the sixth jar is 42.
Step-by-step explanation:
Assume that there are x number of candies in each of the six jars.
⇒ After Alice moves half of the candies from the first jar to the second jar, the number of candies in the second jar is:
[tex]\text{Number of candies in the 2nd jar}=x+\fracx}{2}=\frac{3}{2}x[/tex]
⇒ After Boris moves half of the candies from the second jar to the third jar, the number of candies in the third jar is:
[tex]\text{Number of candies in the 3rd jar}=x+\frac{3x}{4}=\frac{7}{4}x[/tex]
⇒ After Clara moves half of the candies from the third jar to the fourth jar, the number of candies in the fourth jar is:
[tex]\text{Number of candies in the 4th jar}=x+\frac{7x}{4}=\frac{15}{8}x[/tex]
⇒ After Dara moves half of the candies from the fourth jar to the fifth jar, the number of candies in the fifth jar is:
[tex]\text{Number of candies in the 5th jar}=x+\frac{15x}{16}=\frac{31}{16}x[/tex]
⇒ After Ed moves half of the candies from the fifth jar to the sixth jar, the number of candies in the sixth jar is:
[tex]\text{Number of candies in the 6th jar}=x+\frac{31x}{32}=\frac{63}{32}x[/tex]
Now, it is provided that at the end, 30 candies are in the fourth jar.
Compute the value of x as follows:
[tex]\text{Number of candies in the 4th jar}=40\\\\\frac{15}{8}x=40\\\\x=\frac{40\times 8}{15}\\\\x=\frac{64}{3}[/tex]
Compute the number of candies in the sixth jar as follows:
[tex]\text{Number of candies in the 6th jar}=\frac{63}{32}x\\[/tex]
[tex]=\frac{63}{32}\times\frac{64}{3}\\\\=21\times2\\\\=42[/tex]
Thus, the number of candies in the sixth jar is 42.
