The Okonkwo family is budgeting for two fence panels for their garden. The panels are measured against a tape, shown below, each correct to the nearest cent...
Question 1 Report
The Okonkwo family is budgeting for two fence panels for their garden. The panels are measured against a tape, shown below, each correct to the nearest centimetre.
- Write down the error interval for the length of Panel A. (1)
- Work out the lower bound for the total length needed for both panels placed end to end. (2)
- Fencing costs \(\$4.20\) per metre. Work out the upper bound for the total cost of the fencing, correct to the nearest cent. (2)
Answer Details
The tape measure diagram is calibrated from \(0\) to \(200\) cm; reading the ends of the thick bars against the scale gives Panel A as \(182\) cm and Panel B as \(95\) cm, each correct to the nearest centimetre as stated.
(a) A length recorded as \(182\) cm to the nearest cm has true value within half a centimetre either side: \(181.5 \leqslant l < 182.5\) cm. [1 mark]
(b) The lower bound for the total length uses the lower bound of each panel: Panel A's lower bound is \(181.5\) cm and Panel B's (recorded \(95\) cm) is \(94.5\) cm, giving \(181.5 + 94.5 = 276\) cm, which is \(2.76\) m. [2 marks]
(c) The upper bound for the cost needs the upper bound of the length: \(182.5 + 95.5 = 278\) cm \(= 2.78\) m. Multiplying by the price per metre gives the upper bound of the cost: \(2.78 \times 4.20 = \$11.676\), which rounds to the nearest cent as \(\$11.68\). [2 marks]
Notice the pattern: a lower bound on length feeds into a lower bound on total length, but the upper bound on cost needs the upper bound on length, because cost increases as length increases - always check whether the quantity you want increases or decreases with the measurement before choosing which bound to use.
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