Answer:
The number of candies in the sixth jar is 42.
Step-by-step explanation:
Assume that there are <em>x</em> 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](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20candies%20in%20the%202nd%20jar%7D%3Dx%2B%5Cfracx%7D%7B2%7D%3D%5Cfrac%7B3%7D%7B2%7Dx)
⇒ 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](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20candies%20in%20the%203rd%20jar%7D%3Dx%2B%5Cfrac%7B3x%7D%7B4%7D%3D%5Cfrac%7B7%7D%7B4%7Dx)
⇒ 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](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20candies%20in%20the%204th%20jar%7D%3Dx%2B%5Cfrac%7B7x%7D%7B4%7D%3D%5Cfrac%7B15%7D%7B8%7Dx)
⇒ 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](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20candies%20in%20the%205th%20jar%7D%3Dx%2B%5Cfrac%7B15x%7D%7B16%7D%3D%5Cfrac%7B31%7D%7B16%7Dx)
⇒ 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](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20candies%20in%20the%206th%20jar%7D%3Dx%2B%5Cfrac%7B31x%7D%7B32%7D%3D%5Cfrac%7B63%7D%7B32%7Dx)
Now, it is provided that at the end, 30 candies are in the fourth jar.
Compute the value of <em>x</em> 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}](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20candies%20in%20the%204th%20jar%7D%3D40%5C%5C%5C%5C%5Cfrac%7B15%7D%7B8%7Dx%3D40%5C%5C%5C%5Cx%3D%5Cfrac%7B40%5Ctimes%208%7D%7B15%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B64%7D%7B3%7D)
Compute the number of candies in the sixth jar as follows:
![\text{Number of candies in the 6th jar}=\frac{63}{32}x\\](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20candies%20in%20the%206th%20jar%7D%3D%5Cfrac%7B63%7D%7B32%7Dx%5C%5C)
![=\frac{63}{32}\times\frac{64}{3}\\\\=21\times2\\\\=42](https://tex.z-dn.net/?f=%3D%5Cfrac%7B63%7D%7B32%7D%5Ctimes%5Cfrac%7B64%7D%7B3%7D%5C%5C%5C%5C%3D21%5Ctimes2%5C%5C%5C%5C%3D42)
Thus, the number of candies in the sixth jar is 42.