Algebra – Formulae.
    The formula below is used by a cycle hire company to calculate the total cost (C) in pounds (£) of hiring a bicycle. It includes a set upfront fee for each bike plus an hourly rate charged for every hour the bicycle is rented (h).
    C = 10 + 5h

    🙂 = Correct, ☹️ = Incorrect

    💡 Need a quick reminder? Click here for Rules & Tips

    📌 Rules

    • Understand the parts of a real-world formula: A formula uses letters to represent changing quantities and numbers for fixed values. In C = 10 + 5h, 10 is the fixed upfront booking fee, 5 is the hourly rate, h is the number of hours rented, and 5h is the total hourly charge before adding the upfront fee.

    • Calculating total cost (Substitution): Substitute the given number of hours into h. For example, for 3 hours, calculate C = 10 + (5 × 3) = 10 + 15 = £25.

    • Finding hours from a given budget or cost (Solving): Subtract the £10 upfront fee from the total money first, then divide the remaining amount by the hourly rate. For a £35 budget: 35 – 10 = £25, then 25 ÷ 5 = 5 hours.

    💡 Tips

    • Multi-bike and discount calculations: Find the cost per bike first, multiply by the number of bikes, then calculate percentage discounts (e.g. 10% discount means multiplying the total by 0.90 or subtracting 1/10 of the total).

    • Quick typing on our platform: Typing your answer is designed to be super quick and simple! Just type plain numbers like 25 or short answers without adding currency symbols or spaces unless requested.

    ⚠️ Warnings

    • Follow BODMAS/BIDMAS when calculating: Always multiply the hourly rate by hours (5 × h) before adding the £10 fixed fee! Calculating (10 + 5) × h is a common mistake.

    • Watch for rate changes on longer rentals: When a question mentions special deals (such as rates dropping after a set number of hours), break the time into two separate parts before adding the fixed fee.

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    About This Worksheet

    This interactive digital activity provides free, targeted practice on Year 6 Maths. Every question is mapped directly to the Department for Education (DfE) National Curriculum framework for England, helping Key Stage 2 pupils prepare for Paper 1 (Arithmetic) and Papers 2 & 3 (Reasoning) KS2 SATs tests.

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