1510.43 – Ftatateeta's Scarabs


When Ftatateeta died, her will instructed that her massive collection of 1560 scarabs was to be divided among her sister and her sister's 5 sons and 3 daughters, as follows. Each son gets half as much as a daughter gets, and the sister gets twice what a daughter gets.

Tell how many scarabs go to each.

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Solution

If the daughter gets dd, a son gets d2\dfrac{d}{2}, and the sister gets 2d2d. 3d+5(d2)+2d=15603d + 5\left(\dfrac{d}{2}\right) + 2d = 1560; the solution follows along.

The daughter gets 208 scarabs, each son gets 104, and the sister scores 416.

(You can google Ftatateeta.)