A household's weekly shopping bill at the local supermarket, kept carefully in a notebook by one parent, is modelled, in pounds, by \(B = 3(2x + 5) - 2(x - ...
Question 1 Report
A household's weekly shopping bill at the local supermarket, kept carefully in a notebook by one parent, is modelled, in pounds, by \(B = 3(2x + 5) - 2(x - 4)\), where \(x\) is the number of items of fresh produce bought that particular week.
- Expand and simplify the expression for \(B\). (2)
- Work out the value of \(B\) when \(x = 6\). (2)
Answer Details
(a) Expanding \(B = 3(2x + 5) - 2(x - 4)\) means multiplying out each bracket, taking care with the subtraction sign in front of the second bracket. This gives \(6x + 15 - 2x + 8\), and collecting like terms produces \(4x + 23\) [2 marks].
(b) Substituting \(x = 6\) into this simplified expression gives \(B = 4(6) + 23 = 24 + 23 = 47\) [2 marks], so the household's weekly shopping bill that week was 47 pounds. Simplifying first, rather than substituting into the unsimplified formula, reduces the arithmetic needed and the chance of a sign error.
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