Answer:
(i) David: Daniel: Dennis= 2: 3: 7
(ii) David, Daniel and Dennis will get £1000, £1500 and £3500 respectively.
Explanation:
(i) Let the amount of money obtained by David, Daniel and Dennis be x, y and z pounds respectively.
x +y +z= 6000 -----(1)
y= 1.5x -----(2)
z= 3.5x -----(3)
Let's write the amount of money each gets in terms of x.
David --- x
Daniel --- 1.5x
Dennis --- 3.5x
In ratio, David: Daniel: Dennis
= 1: 1.5: 3.5
= 2: 3: 7
This is obtained by multiplying 2 throughout the ratio as ratio is its simplest form is in whole numbers and does not have decimals.
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(ii) Now that we know how the money is shared in terms of ratio, we can easily determine how much each of them receives.
Total amount of money= £6000
Total number of units
= 2u +3u +7u
= 12u
Thus, 12 units represents £6000.
12u ----- £6000
1u ----- £6000 ÷12= £500
Amount of money David will receive
= 2u
= 2(£500)
= £1000
Amount of money Daniel will receive
= 3u
= 3(£500)
= £1500
Amount of money Dennis will receive
= 7u
= 7(£500)
= £3500
Extra notes:
• Units are represented by the letter 'u' in the working. They can also be called parts and their value is in relation to the total amount. Thus if David gets 2 units of the total money, and the total amount is 12 units, he receives 2/12 or ⅙ of the total sum of money.