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Algebra, STD2 EQ-Bank 28

Fried's formula for determining the medicine dosage for children aged 1 - 2 years is:

\(\text{Dosage}=\dfrac{\text{Age of infant (months)}\  \times \ \text{adult dose}}{150}\)

The spreadsheet below is used as a calculator for determining an infant's medicine dosage according to Fried's formula.
 

Amber, a 12 month old child, is being discharged from hospital with two medications. Medicine A has an adult dosage of 325 milligrams and she is to take 26 milligrams. She must also take 9.6 milligrams of Medicine B but the equivalent adult dosage has been left off the spreadsheet.

  1. By using appropriate grid references, write down a formula that could appear in cell B10.   (2 marks)

  2. Calculate the equivalent adult dosage for Medicine B (cell B7) using the information in the spreadsheet.    (2 marks)

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a.    \(=\text{B5}^*\text{B6}/150\)

b.    \(120 \ \text{milligrams}\)

Show Worked Solution

a.     \(=\text{B5}^*\text{B6}/150\)
 

b.    \(\text{Let} \ A= \text{Adult dose}\)

\(\text{Using given formula:}\)

\(9.6\) \(=\dfrac{12 \times A}{150}\)
\(A\) \(=\dfrac{9.6 \times 150}{12}=120 \ \text{milligrams}\)

Algebra, STD2 EQ-Bank 12 MC

Young's formula for determining the medicine dosage for children aged 1 - 12 years is:

\(\text{Dosage} = \dfrac{\text{Age of child (years)}\ \times\ \text{Adult dose}}{\text{Age of child (years) } +\  12}\)

The spreadsheet below is used as a calculator for determining an child's medicine dosage according to Young's formula.

 

Young's formula for calculating an 8 year old child's dosage has been used in cell B9. Using appropriate cell references, the correct formula to input into cell B9 is:

  1. \(=\text{B5}^*\text{B6}/\text{B5}+12\)
  2. \(=(\text{B5}^*\text{B6})/\text{B5}+12\)
  3. \(=\text{B5}^*\text{B6}/(\text{B6}+12)\)
  4. \(=(\text{B5}^*\text{B6})/(\text{B5}+12)\)
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\(D\)

Show Worked Solution

\(=(\text{B5}^*\text{B6})/(\text{B5}+12)\)

\(\Rightarrow D\)

Algebra, STD2 EQ-Bank 26

Fried's formula for determining the medicine dosage for children aged 1 - 2 years is:

\(\text{Dosage}=\dfrac{\text{Age of infant (months)}\  \times \ \text{adult dose}}{150}\)

The spreadsheet below is used as a calculator for determining an infant's medicine dosage according to Fried's formula.
 

  1. By using appropriate grid references, write down a formula that could appear in cell B9.   (2 marks)

  2. Another infant requiring the same medicine has been recommended a dosage of 2 millilitres. What is the age of the infant?   (2 marks)

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a.    \(=\text{B5}^*\text{B6}/150\)

b.    \(15 \ \text{months}\)

Show Worked Solution

a.     \(=\text{B5}^*\text{B6}/150\)
 

b.    \(\text{Let} \ n= \text{age of infant}\)

\(\text{Using given formula:}\)

\(2\) \(=\dfrac{n \times 20}{150}\)
\(n\) \(=\dfrac{2 \times 150}{20}=15 \ \text{months}\)

Algebra, STD2 EQ-Bank 31

Clark's formula for determining the medicine dosage for children is:

\(\text{Dosage}=\dfrac{\text{weight in kilograms}\  \times \ \text{adult dosage}}{70}\)

The spreadsheet below is used as a calculator for determining a child's medicine dosage according to Clark's formula.
 

  1. By using appropriate grid references, write down a formula that could appear in cell E5.   (2 marks)

  2. Another child requiring the same medicine has been recommended a dosage of 62.5 milligrams. How much does the child weigh?   (2 marks)

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a.    \(=\text{B6}^*\text{B5}/70\)

b.    \(17.5 \ \text{kilograms}\)

Show Worked Solution

a.    \(=\text{B6}^*\text{B5}/70\)
 

b.    \(\text{Let} \ w= \text{weight of the child.}\)

\(\text{Using given formula:}\)

\(62.5\) \(=\dfrac{w \times 250}{70}\)
\(w\) \(=\dfrac{62.5 \times 70}{250}=17.5 \ \text{kilograms}\)

Algebra, STD1 A1 2022 HSC 19

Fried's formula is used to calculate the dosage of medication for children aged 1-2 years based on the adult dosage. The formula is

`text{Dosage}=(text{age (in months)} xx\ text{adult dosage})/(150)`.

The adult dosage of a particular medication is 200 mg.

Betty's dosage is calculated to be 24 mg.

How old is Betty in months?   (2 marks)

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`18\ text(months)`

Show Worked Solution

`text{Substituting into the formula:}`

`24` `=( \ text{age} xx 200)/150`  
`text{age}` `=(24 xx 150)/200=360/20`  
  `= 18\ text(months)`  

♦ Mean mark 52%.

Algebra, STD2 A1 2018 HSC 26b

Clark’s formula, given below, is used to determine the dosage of medicine for children.
 

`text(Dosage) = (text(weight in kg × adult dosage))/70`

 
For a particular medicine, the adult dosage is 325 mg and the correct dosage for a specific child is 90 mg.

How much does the child weigh, to the nearest kg?   (2 marks)

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`19\ text(kg)`

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`90 = (text(weight) xx 325)/70`

`:.\ text(weight)` `= (70 xx 90)/325=19.38…`
  `=19\ text(kg  (nearest kg))`
   

Algebra, STD2 A1 EQ-Bank 17

Fried's formula is used to calculate the medicine dosages for children aged 1-2 years.

`text(Child dosage) = {text{Age(in months)}\ xx\ text(adult dosage)}/150`

Ben is 1.5 years old and receives a daily dosage of 450 mg of a medicine.

According to Fried's formula, what would the appropriate adult daily dosage of the medicine be?   (2 marks)

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`3750\ text(mg)`

Show Worked Solution

`text(Substituting into the formula:)`

`450= (18 xx text{adult dosage})/150`

`:.\ text(Adult dosage)= (450 xx 150)/18= 3750\ text(mg)`

Algebra, STD2 A1 2017 HSC 19 MC

Young’s formula, shown below, is used to calculate the dosage of medication for children aged 1−12 years based on the adult dosage.

`D = (yA)/(y + 12)`

where     `D`   = dosage for children aged 1−12 years
`y`   = age of child (in years)
`A`   = Adult dosage

 
A child’s dosage is calculated to be 20 mg, based on an adult dosage of 40 mg.

How old is the child in years?

  1. 6
  2. 8
  3. 10
  4. 12
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`D`

Show Worked Solution

`D= (yA)/(y + 12)`

`20= (40y)/(y + 12)`

`20(y + 12)` `= 40y`
`20y + 240` `= 40y`
`20y` `= 240`
`y` `= 12`

`=> D`

Algebra, STD2 A1 2015 HSC 26b

Clark’s formula is used to determine the dosage of medicine for children.
 

`text(Dosage) = text(weight in kg × adult dosage)/70`
 

The adult daily dosage of a medicine contains 3150 mg of a particular drug.

A child who weighs 35 kg is to be given tablets each containing 525 mg of this drug.

How many tablets should this child be given daily?   (2 marks)

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`3`

Show Worked Solution

`text(Dosage)= (35 xx 3150)/70= 1575\ text(mg)`

`text(# Tablets per day)= text(Dosage)/text(mg per tablet)= 1575/525= 3`

`:.\ text(The child should be given 3 tablets per day.)`

Algebra, STD2 A1 2005 HSC 24b

The formula  `D = (2A)/15`  is used to calculate the dosage of Hackalot cough medicine to be given to a child.

    • D is the dosage of Hackalot cough medicine in millilitres (mL).
    • A is the age of the child in months.
  1. If George is nine months old, what dosage of Hackalot cough medicine should he be given?   (1 mark)

The correct dosage of Hackalot cough medicine for Sam is 4 mL.

  1. What is the difference in the ages of Sam and George, in months?   (3 marks)

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a.    `text(1.2 mL)`

b.    `30`

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a.    `D= (2A)/15= (2 × 9)/15=1.2\ text(mL)`

:.\ text(George should be given a dosage of 1.2 mL)`

 

b.   `text(Find)\ A\ text(when)\ D = text(4 mL)`

`4` `= (2 × A)/15`
 `2A` `= 60`
`A`  `= 30` 

 

`:.\ text(Sam is 30 months old and is 21 months)`

`text(older than George.)`

Algebra, STD2 A1 2014 HSC 4 MC

Young’s formula below is used to calculate the required dosages of medicine for children aged 1–12 years.

 `text(Dosage) = (text(age of child)\ text{(in years)} xx text(adult dosage))/(text(age of child)\ text{(in years)} + 12)`

How much of the medicine should be given to an 18-month-old child in a 24-hour period if each adult dosage is 45 mL? The medicine is to be taken every 6 hours by both adults and children.

  1.       5 mL
  2.    20 mL
  3.    27 mL
  4.    30 mL
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`B`

Show Worked Solution
♦ Mean mark 42%
`text(Dosage)` `= (1.5 xx 45)/(1.5 + 12)`
  `= 5\ text(mL)`

 
`text(S)text(ince 1 dosage every 6 hrs)`

`text(In 24 hours,)`

`text(Medicine given) = 4 xx 5 = 20\ text(mL)`

`=>  B`