Real-world problems questions with answers

Questions

1. Question 1Which phone plan, over a contract?

   Chen Wei needs a new phone and compares the two plans in the table. Chen Wei uses about 35 GB of data a month. Over 24 months, which plan is cheaper? Find the total cost of the cheaper plan over the 24 months.

   	Plan A (with phone)	Plan B (SIM only)
   Monthly fee	$58	$12
   Data each month	20 GB	10 GB
   Extra data	$4 per GB	$5 per GB
   Phone	$98 when you sign up	buy it yourself for $1,199

   Show the worked solution

   1. Step 1: Plan A: the cost each month (in dollars)$58 + (35 - 20) \times 4 = 118$
   2. Step 2: Plan A: the phone + 24 months$98 + 24 \times 118 = 2930$
   3. Step 3: Plan B: the cost each month (in dollars)$12 + (35 - 10) \times 5 = 137$
   4. Step 4: Plan B: the phone + 24 months$1199 + 24 \times 137 = 4487$
   5. Step 5: Compare the totalsPlan A is cheaper: $2,930 over 24 months, $1,557 less than Plan B.
2. Question 2Which electricity retailer?

   The table shows the electricity Kumar's household used in three months. Retailer A charges a fixed price of 26.88 cents per kWh. Retailer B charges 25% less than the tariff of 30.8 cents per kWh. Both prices are before 9% GST. Which retailer is cheaper for these three months? Find the amount the household would pay that retailer, including GST, correct to the nearest cent.

   Month	October	November	December
   Electricity used (kWh)	520	547	498

   Show the worked solution

   1. Step 1: Electricity used in the three months$520 + 547 + 498 = 1565 \text{ kWh}$
   2. Step 2: Retailer A: kWh × price, cents to dollars (÷ 100)$\dfrac{1565 \times 26.88}{100} = 420.672$
   3. Step 3: Retailer B: the price after the discount, then the cost$30.8 \times \dfrac{75}{100} = 23.1 \text{ cents per kWh}$$\dfrac{1565 \times 23.1}{100} = 361.515$
   4. Step 4: The cheaper one, with 9% GST (in dollars)$361.515 \times \dfrac{109}{100} = 394.05135$$\approx 394.05$ (to the nearest cent)Retailer B is cheaper: the household would pay $394.05.
3. Question 3A package tour or on your own?

   A family of 2 adults and 2 children plans a 4-night holiday in Bangkok. They can buy the package tour in the table, or buy return flights and book a hotel themselves. The hotel costs $212 per room per night, and they need 2 rooms. Which option is cheaper? Find the total cost of the cheaper choice.

   	Adult	Child
   Package tour (flights and hotel)	$899	$649
   Return flight only	$389	$289

   Show the worked solution

   1. Step 1: Package tour: adults + children (in dollars)$2 \times 899 + 2 \times 649 = 3096$
   2. Step 2: On their own: the flights$2 \times 389 + 2 \times 289 = 1356$
   3. Step 3: The hotel: price × rooms × nights$212 \times 2 \times 4 = 1696$
   4. Step 4: On their own altogether$1356 + 1696 = 3052$
   5. Step 5: CompareBuying the flights and hotel themselves is cheaper: $3,052 altogether, $44 less.
4. Question 4An excursion: each student's share

   139 students and 6 teachers go on an excursion to the ArtScience Museum. They hire enough buses for everyone, and every student pays for an entrance ticket. The costs are shown in the table. The total cost is shared among the students only, and each student pays the same whole number of dollars, enough to cover the total cost. Find the least amount each student pays.

   Hire of one bus	$495 (49 seats)
   Entrance ticket	$26 per student (teachers free)

   Show the worked solution

   1. Step 1: Number of people$139 + 6 = 145$
   2. Step 2: Buses: everyone needs a seat$\dfrac{145}{49} = 2.959\ldots \rightarrow 3 \text{ buses}$
   3. Step 3: Total cost = buses + tickets (in dollars)$3 \times 495 + 139 \times 26 = 5099$
   4. Step 4: Share among the students, in whole dollars that cover the cost$\dfrac{5099}{139} = 36.683\ldots \rightarrow 37$Each student pays $37 (rounding down would not cover the cost).