Every morning before opening, the shopkeeper counts the coins and notes in the till float, and the total value in pounds after adding \(c\) five-pound notes...
Question 1 Report
Every morning before opening, the shopkeeper counts the coins and notes in the till float, and the total value in pounds after adding \(c\) five-pound notes from the safe is \(35 + 5c\). Head office allows the float to reach no more than £80.
- Write down an inequality in \(c\) using this information. (2)
- Determine how many five-pound notes she can add in total. (2)
Answer Details
This question tests forming and solving an inequality for a maximum allowed total.
- The float value after adding \(c\) five-pound notes is \(35 + 5c\) pounds, and this must not exceed £80: \(35 + 5c \leq 80\). [2]
- Subtract 35 from both sides: \(5c \leq 45\). Divide by 5: \(c \leq 9\). Since \(c \leq 9\) includes equality, the greatest number of five-pound notes she can add is 9. [2]
Exam tip: "no more than" always translates to \(\leq\), not \(<\); this small piece of wording decides whether the final boundary value is included in the answer.
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