IB Mathematics Applications & Interpretation Question Type 2: Formulating and Solving a System of Linear Equations from a Worded Context Exercises

A gardener buys planters of three different sizes: 2 large, 1 medium, and 1 small cost $34; 1 large, 3 medium, and 2 small cost $43; 3 large, 1 medium, and 2 small with a $5 voucher applied cost $49. Find the prices of one large, one medium, and one small planter.

Market baskets cost as follows: 2 oranges, 1 banana, and 1 apple cost $8; 1 orange, 2 bananas, and 2 apples cost $10; 3 oranges, 1 banana, and 4 apples cost $13. Find the price of one orange, one banana, and one apple.

A pizzeria charges a fixed base price plus a per-topping fee. A pizza with 2 toppings costs $14, and a pizza with 5 toppings costs $23. Find the base price and the per-topping fee.

A traveler buys bus and train rides. Two bus rides and one train ride cost $11, and three bus rides with two train rides cost $19. Find the cost of one bus ride and one train ride.

A nut mix is made from almonds and peanuts. A mix containing $1\text{ kg}$ of almonds and $2\text{ kg}$ of peanuts costs $17. A mix containing $3\text{ kg}$ of almonds and $1\text{ kg}$ of peanuts costs $25.

Find the price per kg of almonds and the price per kg of peanuts.

A coffee shop blends beans: 2 kg of Arabica with 1 kg of Robusta costs $26, and 1 kg of Arabica with 3 kg of Robusta costs $29. Find the price per kg of Arabica and Robusta.

At a cinema, two adults and three children pay $38, while three adults and one child pay $36. Find the price of one adult ticket and one child ticket.

At a stationery shop: a pen and two pencils cost $7; two pens, one pencil, and one eraser cost $12; a pen and an eraser cost $7. Find the price of one pen, one pencil, and one eraser.

In a diner, combos are priced as follows: 2 burgers, 1 fries, and 1 drink cost $17; 1 burger, 2 fries, and 2 drinks cost $16; 3 burgers, 1 fries, and 2 drinks with a $4 coupon applied cost $21. Find the price of one burger, one fries, and one drink.

A mobile plan charges a base monthly fee plus a per-GB data cost. One customer used $5\text{ GB}$ and paid $35 total; another customer used $8\text{ GB}$ and paid $44 total.

Find the base fee and the per-GB cost.

Two taxi rides are priced by a fixed start fee plus a per-kilometer charge. A $10\text{ km}$ ride costs $29; a $15\text{ km}$ ride costs $41. Find the start fee and the per-km charge.

At a school store, 4 notebooks and 3 pens cost $51, while 2 notebooks and 5 pens cost $43. Find the price of one notebook and one pen.

A grocery sells shampoos, soaps, and toothpastes. Two shampoos, one soap, and one toothpaste cost $20; one shampoo, two soaps, and three toothpastes cost $28; three shampoos, one soap, and two toothpastes with a $4 loyalty credit cost $24. Find the price of one shampoo, one soap, and one toothpaste.