Jack and Sadia work for a company that sells boxes of breakfast cereal - Edexcel - GCSE Maths - Question 12 - 2018 - Paper 1

Sadia wants to maintain the same 'value for money'. Thus, for her offer, the price per unit of cereal must remain consistent with Jack's idea. The price per unit of cereal with Jack's idea is:

ext{Price per unit for Jack's idea} = rac{p}{1.25x} = rac{p}{1.25} imes rac{1}{x}

Let’s denote the new price Sadia wants to set as $p'$, while keeping the quantity $x$ the same. Therefore:

ext{Price per unit for Sadia's idea} = rac{p'}{x}

Setting both price per unit expressions equal gives us:

rac{p'}{x} = rac{p}{1.25}

This simplifies to:

p' = rac{p}{1.25}

Calculating the required reduction:

ext{Reduction} = p - p' = p - rac{p}{1.25} = p(1 - rac{1}{1.25})

To find the percentage reduction, we compute:

ext{Percentage reduction} = rac{ ext{Reduction}}{p} imes 100 = rac{p(1 - rac{1}{1.25})}{p} imes 100 = (1 - rac{1}{1.25}) imes 100 = (1 - 0.8) imes 100 = 20\%

Thus, Sadia needs to reduce the price by 20%.