Question

In a party if 1 out of 3 guests brought bouquets, 1 out if 5 guests brought gift items, 1 out of 6 gave cash gifts and the remaining 27 guests gave gift vouchers and none of them gave two things. How many people attended the party?

Answer 1

Dear student,


$$\begin{gathered} Letxbethetotalnumberofguests \\ No.ofguestsbroughtbouquets=\frac{1}{3}\times x=\frac{x}{3} \\ No.ofguestsbroughtgiftitems=\frac{1}{5}\times x=\frac{x}{5} \\ No.ofguestsbroughtcashgifts=\frac{1}{6}\times x=\frac{x}{6} \\ Remainingno.ofguests=27 \\ accordingtoquestion, \\ No.ofguestsbroughtbouquets+No.ofguestsbroughtgiftitems+No.ofguestsbroughtcashgifts+Remainingno.ofguests=Totalno.ofguestsattendedtheparty \\ \Rightarrow \frac{x}{3}+\frac{x}{5}+\frac{x}{6}+27=x \\ \Rightarrow x-\left(\frac{x}{3}+\frac{x}{5}+\frac{x}{6}\right)=27 \\ \Rightarrow x-\frac{10x+6x+5x}{30}=27 \\ \Rightarrow x-\frac{21x}{30}=27 \\ \Rightarrow \frac{30x-21x}{30}=27 \\ \Rightarrow \frac{9x}{30}=27 \\ \Rightarrow x=\frac{27\times 30}{9} \\ \Rightarrow x=90 \\ thus,thetotalno.ofguestsattendedthepartyis90 \end{gathered}$$

Regards