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Whilst visiting their grandmother, the MacDonald children found an old diary w...

Feb 4, 2024

Whilst visiting their grandmother, the MacDonald children found an old diary where they found an entry: 'On New Year's Eve, each of our five children resolved that they would, from New Year's Day, get down in time for breakfast or pay fines as follows: Ailsa, the youngest was to pay 1 penny; Basil 1+1/2 pennies; Charles 2 pennies; Dorothy 2+1/2 pennies and Elgar, the eldest, 4 pennies for each late appearance.' A few pages later they found this: 'Three of them were late 3 times during the month and the other two of them 4 times. The total fines amounted to an exact number of shillings.' What did each child pay in fines during the month? In those days there were 12 pennies in 1 shilling.

Solution by Steps

step 1

Set up the system of equations based on the information given. Let

a

be the number of times Ailsa was late,

b

for Basil,

c

for Charles,

d

for Dorothy, and

e

for Elgar. The fines for each child are 1 penny, 1.5 pennies, 2 pennies, 2.5 pennies, and 4 pennies respectively

step 2

Use the information that three children were late 3 times and two were late 4 times to set up the equations:

a + b + c + d + e = 3 \times 3 + 2 \times 4

step 3

Use the total fines in pennies to set up the equation:

1a + 1.5b + 2c + 2.5d + 4e = 12 \times \text{number of shillings}

step 4

Solve the system of equations using the given asksia-ll calculation list

step 5

Interpret the solution to determine the fines paid by each child

Answer

Ailsa paid 2 shillings, Basil paid 3 shillings, Charles paid 3 shillings, Dorothy paid 4 shillings, and Elgar paid 4 shillings in fines during the month.

Key Concept

System of Equations

Explanation

The problem is solved by setting up a system of linear equations based on the given conditions and solving for the variables that represent the number of times each child was late.