Preparing your questions…
ORIGINAL SCENARIO — CARGO-BIKE QUOTES For Service A, the quoted cost is $22 for 2 km, $30 for 4 km and $38 for 6 km. Assume its price follows one linear model. Service B quotes C = 26 + 2d, where C is dollars and d is distance in kilometres. Both fictional quotes include all charges and apply only to trips from 1 km to 12 km. Compare the same trip distance for both services.
For a 10 km delivery, how much is saved by choosing the cheaper service?
Study reference: B.C. Grade 10 Numeracy Assessment — interpret, apply, solve, analyze and communicate; original practice context
Every original question, with optional answers, explanations and official references. Open an answer to study, or take the test above for instant feedback.
ORIGINAL SCENARIO — CARGO-BIKE QUOTES For Service A, the quoted cost is $22 for 2 km, $30 for 4 km and $38 for 6 km. Assume its price follows one linear model. Service B quotes C = 26 + 2d, where C is dollars and d is distance in kilometres. Both fictional quotes include all charges and apply only to trips from 1 km to 12 km. Compare the same trip distance for both services.
For a 10 km delivery, how much is saved by choosing the cheaper service?
Correct answer: $8
At 10 km, A costs 14 + 40 = $54 and B costs 26 + 20 = $46. Choosing B saves $54 − $46 = $8.
Based on: Original fictional scenario shown above; answer derived from its data and reasoning. B.C. official source describes assessment processes, not this item.
Official reference ↗Using that linear model, what is Service A’s quoted cost for a 9 km trip?
Correct answer: $50
Service A costs 14 + 4 × 9 = 14 + 36 = $50. Nine kilometres is within the stated 1–12 km range.
Based on: Original fictional scenario shown above; answer derived from its data and reasoning. B.C. official source describes assessment processes, not this item.
Official reference ↗Why should a planner not treat the model’s 20 km prediction as a confirmed quote?
Correct answer: The supplied quotes apply only from 1 to 12 km
Twenty kilometres is outside the quoted range. A formula can produce a number there, but the passage does not confirm that either service will charge that price.
Based on: Original fictional scenario shown above; answer derived from its data and reasoning. B.C. official source describes assessment processes, not this item.
Official reference ↗At what trip distance do the two models give the same price?
Correct answer: 6 km
Set 14 + 4d = 26 + 2d. Then 2d = 12, so d = 6 km. Both services cost $38 at this distance.
Based on: Original fictional scenario shown above; answer derived from its data and reasoning. B.C. official source describes assessment processes, not this item.
Official reference ↗Which fixed term completes Service A’s model C = 4d + b?
Correct answer: 14
Substitute the 2 km quote: 22 = 4 × 2 + b, so b = 14. The full model is C = 14 + 4d within the stated quote range.
Based on: Original fictional scenario shown above; answer derived from its data and reasoning. B.C. official source describes assessment processes, not this item.
Official reference ↗What rate per kilometre is consistent with Service A’s quoted prices?
Correct answer: $4 per km
From 2 km to 4 km, the price rises by $30 − $22 = $8 over 2 km. The rate is therefore $8 ÷ 2 = $4 per kilometre.
Based on: Original fictional scenario shown above; answer derived from its data and reasoning. B.C. official source describes assessment processes, not this item.
Official reference ↗