A man left 3/7 of his money to his wife, 1/2 of the remainder to his brother, and the rest he divided equally among his three children. If each of his children received $400, how much did his wife receive?
I did this:
Let the money be: x
Wife received: 3/7x
Brother received: x-3/7x = 4/7x
Children: 400*3= 1200
Solution:
x= 3/7x + 4/7x + 1200
Ans: 8400
Wife: 3/7 of 8400= 3600
Please help!
My answer is not coming correct as it is in my workbook.
How can 4/7 come what thing we do to come 4/7
A man left 3/7 of his money to his wife, 1/2 of the remainder to his brother, and the rest he divided equally among his three children. If each of his children received $400, how much did his wife receive?
starting with x,
3/7 went to wife, leaving 4/7
1/2 of that, 2/7, went to brother, leaving 2/7 for his kids.
That 2/7 was 3*400 = 1200
So, 2/7 x = 1200
x = 4200
3/7 of 4200 = 1800
Your mistake was in not noting that the brother only got half of the 4/7.
Why did 2/7 had x with it for tje kids.
Why did 2/7 had x with it for the kids.
To solve this problem, we need to set up an equation based on the given information. Let's break it down step by step.
Let's denote the man's total money as x.
According to the problem,
The man left 3/7 of his money to his wife, which means his wife received (3/7)x.
The remainder, after giving 3/7 to his wife, is (1 - 3/7)x = (4/7)x.
Then, the man gave 1/2 of the remainder to his brother, which means his brother received (1/2) * (4/7)x = (4/14)x.
The remaining money after giving to the brother is (4/7)x - (4/14)x = (8/14)x - (4/14)x = (4/14)x = (2/7)x.
We are given that the remaining money, after dividing among his brother and children, is equally distributed among his three children and each child received $400. Therefore, the total remaining money is $400 * 3 = $1200.
So, we can set up the equation:
(2/7)x = $1200.
To find x, we need to solve this equation. Here's how:
1. Multiply both sides of the equation by 7 to eliminate the fraction:
7 * (2/7)x = 7 * $1200.
(2/7)x = $8400.
2. Multiply both sides of the equation by the reciprocal of 2/7, which is 7/2:
(7/2) * (2/7)x = (7/2) * $8400.
x = $8400.
Therefore, the man's total money is $8400.
To find how much his wife received, substitute the value of x into the equation for the wife's share:
Wife's share = (3/7) * $8400.
= (3/7) * $8400.
= $3600.
Therefore, his wife received $3600.
Double-checking the answer:
The man left 3/7 of $8400, which is $3600, to his wife.
Then, he divided (4/7) * $8400, which is $4800, among his brother and children. Since there are three children, each child received $4800/3 = $1600.
Therefore, the total remaining money distributed to the brother and children is $4800 + $1600 * 3 = $4800 + $4800 = $9600.
Adding the wife's share of $3600 to the remaining money of $9600 gives a total of $3600 + $9600 = $13200 (which is equal to the man's total money, $8400 + $4800).
Thus, our answer is correct.