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Answer to Q127

If the sum of money is divided among ‘n’ children, each child will receive $60. If another child is added to the group and the amount is distributed again each child will receive $50. What is the sum of money to be distributed?

Let the money be = Y

If the sum of money is divided among ‘n’ children, each child will receive $60

Y ÷ n = 60
Y = 60n (eqn 1)

If another child is added to the group and the amount is distributed again each child will receive $50

Y ÷ (n+1) = 50
Y = 50 * (n+1)
Y = 50n + 50 (eqn 2)

putting (eqn 1) into (eqn 2)
60n = 50n + 50
60n - 50n = 50
10n = 50
n = 50 ÷ 10
n = 5

Remember "n" is the number of children, but the question says What is the sum of money to be distributed?. So what will are looking for is Y, not "n".

From (eqn 1)
Y = 60n
Y = 60 * 5
Y = 300

Answer: $300

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570 viewsFeb 11, 2021 at 13:50

Answer to Q127

If the sum of money is divided among ‘n’ children, each child will receive $60. If another child is added to the group and the amount is distributed again each child will receive $50. What is the sum of money to be distributed?

Let the money be = Y

If the sum of money is divided among ‘n’ children, each child will receive $60

Y ÷ n = 60
Y = 60n (eqn 1)

If another child is added to the group and the amount is distributed again each child will receive $50

Y ÷ (n+1) = 50
Y = 50 * (n+1)
Y = 50n + 50 (eqn 2)

putting (eqn 1) into (eqn 2)
60n = 50n + 50
60n - 50n = 50
10n = 50
n = 50 ÷ 10
n = 5

Remember "n" is the number of children, but the question says What is the sum of money to be distributed?. So what will are looking for is Y, not "n".

From (eqn 1)
Y = 60n
Y = 60 * 5
Y = 300

Answer: $300

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