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One day, I visited a sports event where the organizers prepared water bottles for the participants. They discovered that $3$ water dispensers could fill $90$ bottles. To ensure they had enough water for all participants, they needed to determine how many bottles could be filled with different numbers of dispensers.$\newline$(a) How many bottles can be filled with $5$ dispensers? $\newline$i) $150$ $\newline$ii) $120$ $\newline$iii) $100$ $\newline$iv) $160$$\newline$(b) If $4$ dispensers are used, how many bottles can they fill? $\newline$i) $100$ $\newline$ii) $120$ $\newline$iii) $140$ $\newline$iv) $160$$\newline$(c) How many dispensers are needed to fill $180$ bottles? $\newline$i) $6$ $\newline$ii) $5$ $\newline$iii) $8$ $\newline$iv) $7$$\newline$(d) How many dispensers are needed to fill $300$ bottles? $\newline$i) $8$ $\newline$ii) $9$ $\newline$iii) $10$ $\newline$iv) $12$