A market trader spends a fixed amount on stock at the start of the day and sells all of it for exactly double what she paid. She then pays a stall fee of \(...
Question 1 Report
A market trader spends a fixed amount on stock at the start of the day and sells all of it for exactly double what she paid. She then pays a stall fee of \(\pounds15\). Let the amount spent on stock be \(x\) pounds.
- Write an expression, in terms of \(x\), for the amount she receives from selling the stock. (1)
- Give an expression for her profit once the stall fee has been paid. (1)
- Her profit for the day is \(\pounds85\). Use part (b) to write an equation, and solve it to find \(x\). (3)
- State, with a reason, whether her profit is greater than one-fifth of the amount spent on stock. (1)
Answer Details
This question builds up an expression for profit in stages, forms an equation from a known profit figure, solves it, and then compares the result with a fraction of the original spend.
Selling the stock for double what she paid gives revenue:
\[2x\][1 mark]
Profit is revenue minus the amount spent on stock minus the stall fee:
\[2x - x - 15 = x - 15\][1 mark]
Setting this profit equal to \(£85\):
\[x - 15 = 85\]Adding \(15\) to both sides:
\[x = £100\][3 marks]
One-fifth of the \(£100\) spent on stock is \(£20\). Since \(£85 \gt £20\), her profit is greater than one-fifth of the amount spent on stock [1 mark].
Building the profit expression in two steps, first the revenue \(2x\), then subtracting both the cost \(x\) and the stall fee, mirrors exactly how the trader's day unfolds and avoids errors from trying to write the whole thing in one go.
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