Question Type 2: Formulating and solving a system of linear equations from a worded context Exercises

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 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 mobile plan charges a base monthly fee plus a per-GB data cost. One customer used 5 GB and paid $35$ total; another used 8 GB and paid $44$. 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 km ride costs $29$; a 15 km ride costs $41$. Find the start fee and the per-km charge.

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.

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 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 nut mix is made from almonds and peanuts. A 1 kg almond + 2 kg peanut mix costs $17$, and a 3 kg almond + 1 kg peanut mix costs $25$. Find the prices per kg of almonds and peanuts.

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.

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.

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.

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 gardener buys planters: 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.