v1 Algebra, STD2 A1 2023 HSC 36

The following formula can be used to calculate an estimate for blood alcohol content (\(BAC\)) for males.

\(BAC_{\text{male}}=\dfrac{10N-7.5H}{6.8M}\)

\(N\) is the number of standard drinks consumed

\(M\) is the person's weight in kilograms

\(H\) is the number of hours of drinking

Min weighs 70 kg. His \(BAC\) was zero when he began drinking alcohol. At 10:30 pm, after consuming 4 standard drinks, his \(BAC\) was 0.032.

Using the formula, estimate at what time Min began drinking alcohol, to the nearest minute. (4 marks)

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\(7:12\text{ pm}\)

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\(BAC\)	\(=\dfrac{10N-7.5H}{6.8M}\)
\(0.032\)	\(=\dfrac{10\times 4-7.5\times H}{6.8\times 70}\)
\(0.032\times 476\)	\(=40-7.5H\)
\(7.5H\)	\(=40-15.232\)
\(H\)	\(=\dfrac{24.768}{7.5}\)
	\(=3.3024\ \text{hours}\)
	\(\approx 3\ \text{hours}\ 18\ \text{minutes (nearest minute)}\)

\(\text{Time Min began drinking}\)

\(=10:30\text{ pm – 3 h 18 m}\)

\(=7:12\text{ pm}\)

Mean mark 56%.