Variables and expressions Transitional Reasoning Practice

Questions

1. 1.

   In an inter-school mathematics competition, each team is presented with a set of 25 problem-solving questions. A team earns 6 points for every correct response, loses 2 points for every incorrect response, and receives 0 points for any question left unanswered. If a team leaves 5 questions unanswered and answers $c$ questions correctly, which simplified expression represents the team's final score in points?

   • A) $4c - 40$
   • B) $8c - 40$
   • C) $8c - 50$
   • D) $4c + 40$
2. 2.

   An event coordinator arranges identical rectangular banquet tables end-to-end in a single continuous row. A single freestanding table seats 6 guests, but each additional table attached to the row adds 4 seats because the touching ends can no longer be used. If the coordinator configures a row of $n$ connected tables and sets up 3 separate circular tables that each seat 8 guests, which expression represents the total number of guests that can be seated?

   • A) $4n + 26$
   • B) $4n + 30$
   • C) $6n + 24$
   • D) $6n + 18$
3. 3.

   A municipal water conservation reservoir holds an initial reserve of 9,000 cubic meters of water. During a dry weather period lasting 14 days, water is drawn each day for a residential supply of $w$ cubic meters and an agricultural canal that draws 120 cubic meters more than half the daily residential volume. In addition, surface evaporation causes an unavoidable loss of 35 cubic meters of water per day. If no additional water enters the reservoir, which simplified expression represents the volume of water, in cubic meters, remaining in the reservoir at the end of the 14 days in terms of $w$?

   • A) $6830 - 21w$
   • B) $6830 - 42w$
   • C) $8845 - 21w$
   • D) $7320 - 21w$
4. 4.

   An aerial drone survey team maps three designated ecological conservation zones: Zone 1, Zone 2, and Zone 3. The flight time required to survey Zone 1 is $t$ minutes. Surveying Zone 2 requires 18 minutes more than twice the flight time of Zone 1, while surveying Zone 3 requires 25 minutes less than three times the difference in flight time between Zone 2 and Zone 1. Which simplified expression represents the total flight time, in minutes, needed to survey all three zones in terms of $t$?

   • A) $9t + 47$
   • B) $6t + 11$
   • C) $5t + 47$
   • D) $6t + 47$
5. 5.

   A community theater group stages a weekend production, selling $t$ adult tickets at a standard price of 18 dollars each. A student ticket costs 6 dollars less than an adult ticket, and the group sells 25 more than twice the number of adult tickets in student admissions. If the theater incurs a fixed operating cost of 850 dollars for venue rental and scenery, which expression represents the theater's net profit, in dollars, in terms of $t$?

   • A) $42t + 1{,}150$
   • B) $42t - 550$
   • C) $30t - 550$
   • D) $54t - 400$
6. 6.

   A horticultural team prepares organic liquid fertilizer to treat three separate cultivation sectors in a community greenhouse. Sector A receives a base amount of $v$ liters, Sector B requires 12 liters more than twice the amount of Sector A, and Sector C requires 8 liters less than three times the amount of Sector A. In addition to treating the three sectors, the team reserves a fixed amount of 15 liters of fertilizer in a sealed container for subsequent laboratory testing. Which simplified expression represents the total volume of fertilizer, in liters, prepared by the team in terms of $v$?

   • A) $5v + 19$
   • B) $6v - 11$
   • C) $6v + 35$
   • D) $6v + 19$
7. 7.

   An artisan workshop produces handcrafted wooden clocks, where each standard wall clock requires $h$ hours to carve and assemble. A compact desk clock requires 3 hours less than half the time needed for a standard wall clock. In one week, the artisan completes 4 standard wall clocks, 6 compact desk clocks, and spends a fixed total of 8 hours varnishing and packaging the completed pieces. Which simplified expression represents the total number of hours the artisan spends on these tasks during the week in terms of $h$?

   • A) $7h + 5$
   • B) $h + 26$
   • C) $7h - 10$
   • D) $7h + 26$
8. 8.

   A regional youth council receives an annual civic development grant of $G$ dollars to fund three local community initiatives: park revitalization, youth sports, and an environmental workshop series. The council allocates $\frac{1}{5}G + 600$ dollars to the park revitalization initiative. The youth sports initiative is awarded an amount that is 300 dollars greater than twice the allocation of park revitalization. If the entire remaining amount of the annual grant is dedicated to the environmental workshop series, which expression represents the funds, in dollars, allocated to the environmental workshop series in terms of $G$?

   • A) $\frac{3}{5}G + 2100$
   • B) $\frac{2}{5}G + 2100$
   • C) $\frac{2}{5}G - 2100$
   • D) $\frac{2}{5}G - 1500$
9. 9.

   A courier completes different delivery circuits over the course of a work week, where the base circuit driven on Monday has a length of $x$ kilometers. On Tuesday, road maintenance requires an adjusted circuit that is 12 kilometers longer than Monday's circuit. On Wednesday, the courier is assigned an express circuit that is 8 kilometers shorter than twice Monday's circuit. If the courier drives Monday's circuit 2 times, Tuesday's circuit once, and Wednesday's circuit 3 times during the week, which expression represents the total distance driven, in kilometers, in terms of $x$?

   • A) $9x + 4$
   • B) $9x - 12$
   • C) $9x - 36$
   • D) $4x + 4$
10. 10.

    A university technology department installs network switches to connect hardware across a new laboratory wing. Each standard switch connects 12 desktop computers and 4 network printers, while each high-density switch connects 8 laptop docking stations and 2 digital scanners. The department deploys $n$ standard switches, 3 times as many high-density switches as standard switches, and 10 standalone server terminals. Which simplified expression represents the total number of connected devices in terms of $n$?

    • A) $46n + 10$
    • B) $26n + 10$
    • C) $46n + 30$
    • D) $58n + 10$
11. 11.

    A mobile science van carries materials for hands-on workshops, where each large storage crate holds $k$ experimental kits and each of 3 smaller crates holds 4 fewer kits than a large crate. If the van is packed with 5 large crates, the 3 smaller crates, and 7 additional kits set aside as emergency spares, which simplified expression represents the total number of experimental kits on board?

    • A) $8k + 3$
    • B) $8k - 5$
    • C) $8k + 19$
    • D) $8k - 19$
12. 12.

    A landscape architect designs a rectangular garden whose length is 4 meters greater than twice its width, $w$. A paved walking path with a uniform width of 1 meter is constructed completely around the outer boundary of the garden. Which expression represents the total outer perimeter, in meters, of the path in terms of $w$?

    • A) $6w + 12$
    • B) $3w + 8$
    • C) $6w + 8$
    • D) $6w + 16$
13. 13.

    A school robotics club orders materials from a supplier that charges a flat delivery fee of 15 dollars per order and 24 dollars for each robot kit. For every robot kit ordered, the club also purchases 2 expansion sensor packs that cost 3 dollars each. If the club applies a 5-dollar promotional discount coupon to the entire order, which expression represents the total cost, in dollars, of ordering $n$ robot kits?

    • A) $27n + 10$
    • B) $30n + 10$
    • C) $30n + 20$
    • D) $35n - 5$

Answers and step-by-step solutions appear after you finish the test.