Given : Anne buys 600 packets of mints.
Given : Of these 600 packets of mints, 34% are small packets and 40% are large packets.
[tex]:\implies[/tex] Total % of small and large packets is (34 + 40) = 74%
It means : The remaining percentage is of the medium packets of mints which were brought by Anne.
[tex]:\implies[/tex] % of medium packets brought by Anne : (100 - 74) = 26%
[tex]:\implies \textsf{Number of medium packets brought by Anne : $\left(\dfrac{26}{100} \times 600\right)$}[/tex]
[tex]:\implies \textsf{Number of medium packets brought by Anne : $\left(26 \times 6\right)$ = 156}[/tex]
Given : Ben buys 400 packets of mints.
[tex]\textsf{Given : Of these 400 packets of mints, $\dfrac{3}{10}$ are small and $\dfrac{1}{10}$ are large}[/tex]
[tex]\implies \textsf{Total fraction of small and large packets brought by Ben :$\left(\dfrac{3}{10} + \dfrac{1}{10}\right)$}[/tex]
It means : The remaining fraction is of the medium packets of mints which were brought by Ben.
[tex]\implies \textsf{Fraction of medium packets brought by Ben : $\left(1 - \dfrac{3}{10} - \dfrac{1}{10}\right)$}[/tex]
[tex]\implies \textsf{Fraction of medium packets brought by Ben : $\left(1 - \dfrac{4}{10}\right)$ = $\dfrac{6}{10}$}[/tex]
[tex]:\implies \textsf{Number of medium packets brought by Ben : $\left(\dfrac{6}{10} \times 400\right)$}[/tex]
[tex]:\implies \textsf{Number of medium packets brought by Anne : $\left(6 \times 40\right)$ = 240}[/tex]
Given : Chas buys 210 small packets of mints.
Given : Number of small packets : number of medium packets = 3 : 4
[tex]\implies \mathsf{\dfrac{210}{number \ of \ medium \ packets} = \dfrac{3}{4}}[/tex]
[tex]\implies \mathsf{Number \ of \ medium \ packets = \left(210 \times \dfrac{4}{3}\right)}[/tex]
[tex]\implies \textsf{Number of medium packets brought by Chas = 280}[/tex]
Total number of medium packets of mints brought by these three shop keepers (Anne, Ben, Chas) are :
[tex]:\implies[/tex] (156 + 240 + 280)
[tex]:\implies[/tex] 676
