Adults before the bus

MediumBrainteasers~7m

At a concert, $\tfrac{5}{12}$ of the attendees are adults. A bus carrying $50$ people then arrives, and afterwards $\tfrac{11}{25}$ of the attendees are adults. What is the minimum number of adults who could have been at the concert before the bus arrived?

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Let $T$ = attendees before ( $12\mid T$ ) and $a$ = adults on the bus. Write the after-fraction equation.
You get $T=(300a-6600)/7$ ; use integrality ( $a\equiv1\bmod 7$ , $a\ge22$ ) to find the smallest valid case.

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Adults before the bus

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