A father left all of his money to his 3 children. Child A received 1/6 of his father's money while Child B received 1/7. Child C, who received the remainder of the money , was given $23,490. How much did Child A receive?

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A father left all of his money to his 3 children. Child A received 1/6 of his father's money while Child B received 1/7. Child C, who received the remainder of the money , was given $23,490. How much did Child A receive?

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Answer 1 · 2017-10-18T01:42:41

See a solution process below:

Explanation:

First, we need to determine what "slice" of the money Child C received:

Let's call the "slice" Child C received: $c$ $c$

100% is the same as 1 so we can write and solve this equation for $c$ $c$ ;

$\frac{1}{6} + \frac{1}{7} + c = 1$ $1/6 + 1/7 + c = 1$

$(\frac{7}{7} \times \frac{1}{6}) + (\frac{6}{6} \times \frac{1}{7}) + c = 1$ $(7/7 xx 1/6) + (6/6 xx 1/7) + c = 1$

$\frac{7}{42} + \frac{6}{42} + c = 1$ $7/42 + 6/42 + c = 1$

$\frac{7 + 6}{42} + c = 1$ $(7 + 6)/42 + c = 1$

$\frac{13}{42} + c = 1$ $13/42 + c = 1$

$\frac{13}{42} - \frac{13}{42} + c = 1 - \frac{13}{42}$ $13/42 - color(red)(13/42) + c = 1 - color(red)(13/42)$

$0 + c = \frac{42}{42} - \frac{13}{42}$ $0 + c = 42/42 - color(red)(13/42)$

$c = \frac{42 - 13}{42}$ $c = (42 - color(red)(13))/42$

$c = \frac{29}{42}$ $c = 29/42$

Child C received $\frac{29}{42}$ $29/42$ of his father's money.

Now, let's call the total amount of money the father left for the 3 children: $a$ $a$

We can write this equation and solve for $a$ $a$ :

$\frac{29}{42} \times a = $ 23490$ $29/42 xx a = $23490$

$\frac{42}{29} \times \frac{29}{42} \times a = \frac{42}{29} \times $ 23490$ $color(red)(42)/color(blue)(29) xx 29/42 xx a = color(red)(42)/color(blue)(29) xx $23490$

$cancel(color(red)(42))/cancel(color(blue)(29)) xx color(blue)(cancel(color(black)(29)))/color(red)(cancel(color(black)(42))) xx a = color(red)(42)/color(blue)(29) xx ($810 xx 29)$

$a = color(red)(42)/cancel(color(blue)(29)) xx ($810 xx color(red)(cancel(color(black)(29))))$

$a = color(red)(42) xx $810$

$a = $34020$

We now know the total amount of money the father left to all the children was $34,020.

Child A received $1/6$ of this money:

$1/6 xx $34020 =>$

$1/6 xx $5670 xx 6 =>$

$1/color(red)(cancel(color(black)(6))) xx $5670 xx color(red)(cancel(color(black)(6))) =>$

$$5670$

Child A received $5,670

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A father left all of his money to his 3 children. Child A received 1/6 of his father's money while Child B received 1/7. Child C, who received the remainder of the money , was given $23,490. How much did Child A receive?

1 Answer

Explanation:

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