SOLUTION: The sum of $224 was divided among 3 people so that the second person received $1 less than twice as much as the first, and the third received $11 more than the second. How much did

Question 352146: The sum of $224 was divided among 3 people so that the second person received $1 less than twice as much as the first, and the third received $11 more than the second. How much did each person received?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The sum of $224 was divided among 3 people so that the second person received $1
less than twice as much as the first, and the third received $11 more than the second.
How much did each person received?
:
Let the three people be x, y, z
:
Write an equation for each statement:
:
"the second person received $1 less than twice as much as the first,"
y = 2x - 1
:
"the third received $11 more than the second."
z = y + 11
From the 1st equation replace y with (2x-1) in the above equation
z = (2x-1) + 11
z = 2x + 10
:
"The sum of $224 was divided among 3 people"
x + y + z = 224
Replace y and z
x + (2x-1) + (2x + 10) = 224
5x + 9 = 224
5x = 224 - 9
5x = 215
x =
x = $43
then
y = 2(43)-1
y = 86 - 1
y = $85
and
z = 2(43) + 10
z = 86 + 10
z = $96
:
:
See if this adds up
43 + 85 + 96 = 224
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