Question

A man divided $9,000 among his wife, son, and daughter. The wife received twice as much as the daughter, and the son received $1,000 more than the daughter. How much did each receive?

Answer 1

let x be the amount the wife received
y be the amount for the daughter
z for the son
Since the total amount is 9,000 then
x + y + z =9,000 ----equation 1
From the statement
"The wife received twice as much as the daughter"
x = 2y -----equation 2

"the son received $1,000 more than the daughter"
z = y +1000 -----equation 3

substitute equations 2 and 3 to equation 1
x + y + z =9,000
2y + y + y + 1000 = 9,000
4y = 9,000 - 1,000
4y = 8000
y = 2,000

substitute to equations 2 and 3
x = 2y
x = 2(2,000)
x = 4,000

z = y + 1000
z = 2,000 + 1,000
z = 3,000