Sam gave ¹₁₀ of his marbles to Harry, ¹₉ of his remaining marbles to Jenson and ¹₆ of the rest of his marbles to Riordan. He then had 160 marbles left. How many marbles had he at first?
Fraction of the rest of the marbles that Sam had left after giving to Harry, Jenson and Riordan
= 1 - ¹₆
= ⁵₆

⁵₆ of the rest of the marbles that Sam had left = 160
¹₆ of the rest of the marbles that Sam had left = 160 ÷ 5 = 32
⁶₆ of the rest of the marbles that Sam had left = 6 x 32 = 192

Fraction of his remaining marbles that Sam had left after giving to Harry and Jenson
= 1 - ¹₉
= ⁸₉

⁸₉ of his remaining marbles that Sam had left = 192
¹₉ of his remaining marbles that Sam had left = 192 ÷ 8 = 24
⁹₉ of his remaining marbles that Sam had left = 9 x 24 = 216

Fraction of his remaining marbles that Sam had left after giving to Harry
= 1 - ¹₁₀
= ⁹₁₀

⁹₁₀ of the marbles that Sam had left = 216
¹₁₀ of the marbles that Sam had left = 216 ÷ 9 = 24
¹⁰₁₀ of the marbles that Sam had left = 10 x 24 = 240

Number of marbles that Sam had at first = 240

Answer(s): 240