Question 125283: Can you please solve this problem?
Anna, Jennifer, and Mia have certain sums of money. If Anna gives Jennifer $100, they will have the same amount; if Anna gives Mia $100, Mia will have twice as much as Anna; if Jennifer gives Mia $100, Mia will have 4 times as much as Jennifer. What sum has each?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Anna, Jennifer, and Mia have certain sums of money. If Anna gives Jennifer $100, they will have the same amount; if Anna gives Mia $100, Mia will have twice as much as Anna; if Jennifer gives Mia $100, Mia will have 4 times as much as Jennifer. What sum has each?
:
Let a = Anna$; j = Jenn$; m = Mia$
:
Write an equation for equation for each statement:
:
"If Anna gives Jennifer $100, they will have the same amount;"
a - 100 = j + 100
or
j + 100 = a - 100
j = a - 100 - 100
j = a - 200
:
"if Anna gives Mia $100, Mia will have twice as much as Anna;"
m + 100 = 2(a - 100)
m + 100 = 2a - 200
m = 2a - 200 - 100
m = 2a - 300
:
"if Jennifer gives Mia $100, Mia will have 4 times as much as Jennifer."
m + 100 = 4(j-100)
m + 100 = 4j - 400
m = 4j - 400 - 100
m = 4j - 500
:
In the above equation, substitute (a-200) for j and (2a-300) for m; solve for a
(2a-300) = 4(a-200) - 500
2a - 300 = 4a - 800 - 500
2a - 300 = 4a - 1300
-300 + 1300 = 4a - 2a
1000 = 2a
a = 
a = $500
:
m = 2a - 300
Substitute 500 for a
m = 2(500) - 300
m = 1000 - 300
m = 700
:
Use m = 4j - 500 to find j; substitute 700 for m
700 = 4j - 500
700 + 500 = 4j
1200 = 4j
j = 
j = 300
:
Anna had $500; Mia had $700 and Jenn had $300
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