Notebooks cost \($2.40\) each. Amir has \($20\) and buys \(n\) notebooks. (a) Write down an inequality, in terms of \(n\), for the cost of the notebooks. [1...
Question 1 Report
Notebooks cost \($2.40\) each.
Amir has \($20\) and buys \(n\) notebooks.
(a) Write down an inequality, in terms of \(n\), for the cost of the notebooks. [1]
(b) Work out the greatest number of notebooks Amir can buy. [2]
(c) Work out how much money Amir has left when he buys this number of notebooks. [1]
Answer Details
(a) Each notebook costs \(\$2.40\), so \(n\) notebooks cost \(2.40n\) dollars. Amir cannot spend more than he has, though he may spend it all exactly, so the cost is at most \(\$20\):
\[ 2.40n\le 20 \] [B1]
(b) Divide both sides by \(2.40\):
\[ n\le\frac{20}{2.40}=8.33\ldots \] [M1]
The number of notebooks must be a whole number, and \(n\) has to stay below \(8.33\ldots\), so the largest possible value is
\[ n=8 \] [A1]
(c) Eight notebooks cost \(8\times 2.40=\$19.20\), so the money left is
\[ 20-19.20=\$0.80 \] [B1]
The important step in part (b) is rounding down rather than to the nearest whole number. Rounding \(8.33\ldots\) to \(8\) happens to agree with normal rounding, but the reason is the context: \(9\) notebooks would cost \(\$21.60\), which Amir cannot afford. Part (c) then confirms that \(8\) is right, since the money left over is less than the price of one more notebook.
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