Ben gave ¹₈ of his beads to Ethan, ¹₇ of his remaining beads to Vaidev and ¹₅ of the rest of his beads to Zane. He then had 120 beads left. How many beads had he at first?
Fraction of the rest of the beads that Ben had left after giving to Ethan, Vaidev and Zane
= 1 - ¹₅
= ⁴₅

⁴₅ of the rest of the beads that Ben had left = 120
¹₅ of the rest of the beads that Ben had left = 120 ÷ 4 = 30
⁵₅ of the rest of the beads that Ben had left = 5 x 30 = 150

Fraction of his remaining beads that Ben had left after giving to Ethan and Vaidev
= 1 - ¹₇
= ⁶₇

⁶₇ of his remaining beads that Ben had left = 150
¹₇ of his remaining beads that Ben had left = 150 ÷ 6 = 25
⁷₇ of his remaining beads that Ben had left = 7 x 25 = 175

Fraction of his remaining beads that Ben had left after giving to Ethan
= 1 - ¹₈
= ⁷₈

⁷₈ of the beads that Ben had left = 175
¹₈ of the beads that Ben had left = 175 ÷ 7 = 25
⁸₈ of the beads that Ben had left = 8 x 25 = 200

Number of beads that Ben had at first = 200

Answer(s): 200