Question

Each of six jars contains the same number of candies. Alice moves half of the candies from the first jar to the second jar. Then Boris moves half of the candies from the second jar to the third jar. Then Clara moves half of the candies from the third jar to the fourth jar. Then Dara moves half of the candies from the fourth jar to the fifth. Finally, Ed moves half of the candies from the fifth jar to the sixth jar. At the end, 30 candies are in the fourth jar.
How many candies are now in the sixth jar?

Answer 1

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:

$\text{Number of candies in the 2nd jar}=x+\fracx}{2}=\frac{3}{2}x$

⇒ After Boris moves half of the candies from the second jar to the third jar, the number of candies in the third jar is:

$\text{Number of candies in the 3rd jar}=x+\frac{3x}{4}=\frac{7}{4}x$

⇒ After Clara moves half of the candies from the third jar to the fourth jar, the number of candies in the fourth jar is:

$\text{Number of candies in the 4th jar}=x+\frac{7x}{4}=\frac{15}{8}x$

⇒ After Dara moves half of the candies from the fourth jar to the fifth jar, the number of candies in the fifth jar is:

$\text{Number of candies in the 5th jar}=x+\frac{15x}{16}=\frac{31}{16}x$

⇒ After Ed moves half of the candies from the fifth jar to the sixth jar, the number of candies in the sixth jar is:

$\text{Number of candies in the 6th jar}=x+\frac{31x}{32}=\frac{63}{32}x$

Now, it is provided that at the end, 30 candies are in the fourth jar.

Compute the value of x as follows:

$\text{Number of candies in the 4th jar}=40\\\\\frac{15}{8}x=40\\\\x=\frac{40\times 8}{15}\\\\x=\frac{64}{3}$

Compute the number of candies in the sixth jar as follows:

$\text{Number of candies in the 6th jar}=\frac{63}{32}x$

                                                    $=\frac{63}{32}\times\frac{64}{3}\\\\=21\times2\\\\=42$

Thus, the number of candies in the sixth jar is 42.