Fraction word problems — find total (ACT). Game on.

For a school fundraiser, students sold raffle tickets in four ways. Exactly $\dfrac{1}{5}$ of the tickets were sold at a walk-up table, exactly $\dfrac{1}{6}$ were sold during a pre-sale, $24$ tickets were sold by mail, and $14$ tickets were sold at the school office. How many raffle tickets were sold in all?

At the start of the season, a soccer club roster was divided into three position groups. Exactly $\dfrac{1}{3}$ of the players were forwards, exactly $\dfrac{1}{2}$ were midfielders, and $9$ players were goalkeepers. How many players were on the roster?

An arena concert used four seating sections. Exactly $\dfrac{1}{6}$ of the seats were in section A, exactly $\dfrac{1}{3}$ were in section B, $22$ seats were in section C, and $18$ seats were in section D. How many seats were in the arena for this concert?

A botanical garden is divided into four planted areas. Exactly $\dfrac{1}{4}$ of the garden is vegetables, exactly $\dfrac{1}{5}$ is flowers, $48$ square meters are herbs, and $40$ square meters are fruit trees. How many square meters are in the entire garden?

A warehouse manager sorted a shipment of shirts into four color groups. Exactly $\dfrac{1}{5}$ of the shirts were red, exactly $\dfrac{1}{4}$ were white, $42$ shirts were green, and $24$ shirts were blue. How many shirts were in the shipment?

A public library counted every book checked out on one busy Saturday. Exactly $\dfrac{1}{6}$ of the checkouts were fiction, exactly $\dfrac{1}{2}$ were nonfiction, $14$ checkouts were reference books, and $10$ checkouts were magazines. How many books were checked out that day?

A car dealership's lot held four types of vehicles. Exactly $\dfrac{1}{3}$ of the vehicles were sedans, exactly $\dfrac{1}{4}$ were SUVs, $45$ vehicles were compacts, and $35$ vehicles were trucks. How many vehicles were on the lot?

A catering company prepared a buffet with five labeled sections. Exactly $\dfrac{1}{5}$ of the servings were breakfast items, exactly $\dfrac{1}{4}$ were lunch items, exactly $\dfrac{1}{10}$ were snacks, $27$ servings were dinner items, and $18$ servings were desserts. How many servings were prepared in all?