Question 271128: My son is in Honors Algebra in the 8th grade. I'm trying to help him figure this problem out but can't seem to get it. Please help.
If Alex gives Bobby $4, then Alex would have half as much money as Bobby. If Bobby gives Chris $7, then Chris would have $35 more than Bobby. If Chris gives Alex $17, then Alex would have $1 more than Chris.
How many dollars does each person have?
Thanks for your assistance.
Sincerely,
Will Schultz
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let a = amount of money alex has originally.
let b = amount of money bobby has originally.
let c = amount of money chris has originally.
If Alex give Bobby $4, then Alex would have half as much money as Bobby.
Equation we get is:
(a-4) = (b+4)/2
multiply both sides of these equations by 2 to get:
2a-8 = b+4
subtract 4 from both sides of this equations to get:
b = 2a-12
If Bobby gives Chris 7, then Chris would have $35 more than Bobby.
equation we get is:
(c+7) = (b-7) + 35
subtract 7 from both sides of this equation to get:
c = b-7+35-7 which becomes:
c = b + 21
If Chris gives Alex 17, then Alex would have 1 more than Chris.
Equation we get is:
a+17 = c-17 + 1
subtract 17 from both sides of this equation to get:
a = c-17+1-17 which becomes:
a = c-33
We have 3 equations to work with.
They are:
b = 2a-12 (first equation)
c = b + 21 (second equation)
a = c-33 (third equation)
substitute 2a-12 for b in the second equation to get:
c = (2a-12) + 21 which becomes:
c = 2a-12+21 which becomes:
c = 2a + 9
substitute 2a+9 for c in the third equation to get:
a = (2a+9)-33 which becomes:
a = 2a+9-33 which becomes:
a = 2a-24
subtract a from both sides of this equation and add 24 to both sides of this equation to get:
a = 24 ***********************************************************
substitute 24 for a in the first equation to get:
b = 2*24-12 which becomes:
b = 48-12 which becomes:
b = 36 ***********************************************************
substitute 36 for b in the second equation to get:
c = 36 + 21 which becomes:
c = 57 ***********************************************************
we get:
a = 24
b = 36
c = 57
Now to see if this is accurate.
Equation from the first transaction is:
(a-4) = (b+4)/2
substitute 24 for a and 36 for b to get:
24-4 = 36+4/2 which becomes:
20 = 40/2 which is true !!!!!
Equation from the second transaction is:
(c+7) = (b-7) + 35
substitute 57 for c and 36 for b to get:
57+7 = 36-7 + 35 which becomes:
64 = 29 + 35 which becomes:
64 = 64 which is true !!!!!
Equation from the third transaction is:
a+17 = c-17 + 1
substitute 24 for a and 57 for c to get:
24+17 = 57-17+1 which becomes:
41 = 41 which is true !!!!!
All equations are true so the answers must be good.
Answers are:
Alex has $24
Bobby has $36
Chris has $57
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