SOLUTION: How do you turn "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 sec

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: How do you turn "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 sec      Log On


   

Question 488399: How do you turn "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 receive?" into an equation?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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How do you turn "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 receive?" into an equation?
:
The amt three people receive: a, b, c
write an equation for each statement.
:
"The sum of $224 was divided among 3 people"
a + b = c = 224
:
"the second person received $1 less than twice as much as the first,"
b = 2a - 1
solve this equation for a
2a = b + 1
a = %28b%2B1%29%2F2
:
" the third received $11 more than the second."
c = b + 11
:
Replace a and c in the 1st equation
%28b%2B1%29%2F2 + b + (b+11) = 224
get rid of the fraction multiply eq by 2
b + 1 + 2b +2(b+11) = 2(224)
b + 1 + 2b + 2b + 22 = 448
5b + 23 = 448
5b = 448 - 23
3b = 425
b = 425/5
b = $85 is b's share
the
a = %2885%2B1%29%2F2
a = $43 is a's share
and
c = 85 + 11
c = $96 is c's share
:
:
Check this; find the total
43 + 85 + 96 = 224