Solve fixed and variable vehicle-cost problems

Ontario Grade 11 Mathematics

Transportation and Travel

Grade 11 workplace mathematics • MEL3E study topic C1.7

Buying or using a vehicle can involve costs that stay the same and costs that change with use. A monthly insurance payment may be due whether a vehicle travels a little or a lot. Fuel costs usually rise when the vehicle travels farther. Knowing the difference helps with everyday choices, such as estimating a monthly budget or comparing two vehicles. This lesson uses simple arithmetic and repeated calculations to solve those problems. All amounts are in Canadian dollars (CAD).

What you will learn

Identify fixed and variable costs in a vehicle-cost problem.
Use a calculator or spreadsheet to find vehicle costs for a chosen period or distance.
Compare vehicle costs using clear, repeated calculations.

1. Sort the costs

A fixed cost stays the same for the period in the problem, even if the vehicle is driven more or less. For example, if insurance costs CAD 180 each month, that monthly payment is a fixed cost for the budget period. A variable cost changes with how much the vehicle is used. Fuel is a common example: more kilometres usually mean more fuel and a higher fuel cost.

The time period or distance matters. A cost can be fixed for one kind of comparison and not for another. A monthly parking pass may be fixed for a monthly budget. Paying for parking each day instead may make the total depend on the number of days. Always read what the problem says before sorting costs.

A vehicle may also have several variable costs, such as fuel and maintenance that is charged by distance. Some problems provide a variable cost per kilometre directly. Others provide fuel use and a fuel price, so you calculate the fuel cost for the distance. Use only the information provided; do not guess costs that are missing.

Fixed cost: stays the same for the stated period.
Variable cost: changes with distance or amount of use.
Check the period and the units, such as per month, per litre, or per kilometre.

2. Calculate costs with a calculator or spreadsheet

First list each cost and its unit. If a problem gives a cost per kilometre, multiply that rate by the number of kilometres. For example, a vehicle driven 600 km at CAD 0.14 per kilometre has a variable cost of CAD 84. The units help show why multiplication works: the kilometre units cancel, leaving a cost.

When the problem gives fuel use in litres per 100 km, calculate the litres needed for the distance. Divide the distance by 100, then multiply by the stated litres per 100 km. Next, multiply the litres by the fuel price per litre. Keep the steps separate and round money to the nearest cent when needed.

Add fixed costs and variable costs to get the total for the stated period. A spreadsheet can help when you need totals for several distances. Put the fixed cost in one column, the distance in another, and the variable cost and total in further columns. Enter the same arithmetic you would do by hand, then check that the units and results make sense.

total vehicle cost=fixed costs+variable costs

Use rate times amount when a cost is given per kilometre.
For fuel use, calculate litres first, then multiply by price per litre.
Total cost is the sum of the relevant fixed and variable costs.

3. Compare options fairly

To compare vehicles, use the same period and the same distance for each one. Include only the costs the problem provides, and sort them in the same way for both options. If one option has a lower fixed cost but a higher variable cost, neither is automatically cheaper. The distance driven can affect which total is lower.

Choose a few realistic distances, calculate each vehicle’s total at those distances, and compare the results. A calculator or spreadsheet is useful because it makes repeated calculations easier. If the totals are close, check the arithmetic and make sure no cost has been counted twice or left out.

A cost estimate is only as complete as its information. If a problem gives monthly insurance and fuel cost but does not give repair or parking costs, the total is for the listed costs only. State that clearly when explaining your comparison.

Compare the same time period and distance.
A lower fixed cost does not always mean a lower total cost.
Describe what is included in an estimate.

Vehicle cost comparison

Distance in one month	Vehicle A total	Vehicle B total	Lower listed cost
500 km	CAD 230	CAD 250	Vehicle A
1,200 km	CAD 356	CAD 320	Vehicle B

Worked example

Example 1: Monthly vehicle budget

Jordan drives 800 km in a month. Insurance costs CAD 165 per month. The vehicle’s fuel and routine-use costs are estimated at CAD 0.12 per kilometre. Find the listed monthly total.

Identify the costs
Insurance is fixed for this monthly budget because the amount is stated per month. The per-kilometre amount is variable because it depends on distance driven.
Calculate variable cost
Multiply the distance by the cost per kilometre. The kilometre units cancel, leaving a cost amount.
$800\times\text{CAD }0.12=\text{CAD }96$
Add the fixed cost
Add the variable cost to the monthly insurance payment. This gives the total for the costs listed in the problem.
$\text{CAD }165+\text{CAD }96=\text{CAD }261$

Answer: The listed monthly vehicle cost is CAD 261.

Check: At 800 km, the variable cost is under CAD 100, so adding it to CAD 165 gives a total just over CAD 250. CAD 261 is reasonable.

Worked example

Example 2: Compare two vehicles at different distances

Two vehicles are being considered for a one-month work commute. Vehicle A has CAD 140 in monthly fixed costs and a variable cost of CAD 0.18 per kilometre. Vehicle B has CAD 200 in monthly fixed costs and a variable cost of CAD 0.10 per kilometre. Compare their listed monthly costs at 500 km and 1,200 km.

Calculate Vehicle A at 500 km
Multiply the distance by its variable rate, then add its fixed monthly cost.
$500\times\text{CAD }0.18+\text{CAD }140=\text{CAD }230$
Calculate Vehicle B at 500 km
Use the same distance so the comparison is fair. Add Vehicle B’s fixed cost to its variable cost for 500 km.
$500\times\text{CAD }0.10+\text{CAD }200=\text{CAD }250$
Calculate Vehicle A at 1,200 km
Repeat the same steps at the higher distance. The fixed cost stays CAD 140, while the variable cost changes with kilometres.
$1{,}200\times\text{CAD }0.18+\text{CAD }140=\text{CAD }356$
Calculate Vehicle B at 1,200 km
Multiply 1,200 km by Vehicle B’s rate and add its monthly fixed cost.
$1{,}200\times\text{CAD }0.10+\text{CAD }200=\text{CAD }320$

Answer: At 500 km, Vehicle A costs CAD 230 and Vehicle B costs CAD 250, so Vehicle A is cheaper by CAD 20. At 1,200 km, Vehicle A costs CAD 356 and Vehicle B costs CAD 320, so Vehicle B is cheaper by CAD 36.

Check: At the lower distance, Vehicle A’s fixed-cost advantage matters more. At the higher distance, Vehicle B’s lower per-kilometre cost reduces its total enough to make it cheaper.

Common mistakes and how to avoid them

Treating every vehicle cost as fixed.

Correction: Check whether the amount stays the same for the period or changes with distance or use.

Adding the per-kilometre rate directly to a fixed cost.

Correction: Multiply the per-kilometre rate by the distance first. Then add the resulting cost.

Comparing vehicles at different distances or periods.

Correction: Use the same distance and time period for both options.

Assuming a calculated total includes costs that were not provided.

Correction: Say that the total covers only the listed costs. Do not add unsupported estimates.

Lesson summary

Fixed costs stay the same for the stated period; variable costs change with use.
Multiply a cost per kilometre by the distance driven.
For fuel-use problems, calculate litres needed and then multiply by the price per litre.
Add the listed fixed and variable costs to find a total.
Compare vehicle options using the same period and distance.

Check your understanding

Question 1

A vehicle has monthly insurance of CAD 190 and a variable cost of CAD 0.15 per kilometre. What is the listed total cost for 400 km?

CAD 205
CAD 250
CAD 250? No; CAD 60 variable plus CAD 190 fixed equals CAD 250.
CAD 790

Show answer and explanation

CAD 250? No; CAD 60 variable plus CAD 190 fixed equals CAD 250.

The variable cost is 400 times CAD 0.15, or CAD 60. Add the fixed CAD 190 to get CAD 250. The matching option states that result.

Question 2

Which statement best describes a fixed vehicle cost in a monthly budget?

It rises every time the vehicle travels another kilometre.
It stays the same for the month, even if distance changes.
It is always the same as the fuel cost.
It must be excluded from the total.

Show answer and explanation

It stays the same for the month, even if distance changes.

A fixed cost stays the same for the stated period. In this question, the period is one month.

Key terms

Fixed cost: A cost that stays the same for the period named in the problem.
Variable cost: A cost that changes with distance driven or another measure of vehicle use.
Rate: An amount for each unit, such as a cost for each kilometre.
Estimate: A calculated amount based on the information available; it may not include costs that were not provided.

Continue through MEL3E

View the complete MEL3E Ontario Grade 11 Mathematics curriculum and lessons

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 11 Mathematics (MEL3E), expectation C1.7. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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