Doctors sometimes need to work out how much medicine to give a child, based on the correct dose for an adult - Leaving Cert Mathematics - Question 7 - 2012

For Young's rule: The formula is:

$C = \frac{Y}{Y + 12} \times A$

where:

• C = child's dose
• Y = child's age in years
• A = adult's dose

For Young's rule: The formula is:

$C = \frac{A \times Y}{Y + 12}$

where:

• C = child's dose
• Y = child's age in years
• A = adult's dose

For the third version of Young's rule: The formula is:

$C = \frac{4 \times Y}{Y + 12} \times A$

where:

• C = child's dose
• A = adult's dose
• Y = child's age in years

All three formulae can be manipulated algebraically to show they yield the same result. Specifically, rearranging each formula leads them to the common form:

$C = \frac{YA}{Y + 12}$

This equivalence demonstrates that they all accurately compute the child's dosage based on the adult dosage adjusted by the child's age.

Using Young's rule:

$C = \frac{Y \times A}{Y + 12}$

Substituting the values:

$C = \frac{6 \times 150}{6 + 12} = \frac{900}{18} = 50 ext{ mg per day}$

Thus, the correct dose for a six-year-old child is 50 mg.

Given that the child receives one fifth of the adult dose:

Using Young's rule,

$C = \frac{YA}{Y + 12}$

Since C is one fifth of the adult dose:

rac{A}{5} = \frac{YA}{Y + 12}

This leads to:

Using the BSA rule to calculate the correct dose:

$C = \frac{\text{BSA}}{173} \times A$

From the chart, at height of 125 cm and weight of 26 kg, the BSA is approximately 0.95 m²:

$C = \frac{0.95}{173} \times 200$

Calculating this gives:

$\approx 110 mg$

So, the correct dose using BSA is approximately 110 mg.

Given:

• Clark's and Young's rules both give a dose of 90 mg.
• BSA gives a dose of 130 mg.

Based on Young's rule and solving: