Question 234020: I think this will be a linear equation, but I'm not sure. I don't even know where to begin. Can you please help? The problem is:
John says to Brenda, "If you give me $7, we will have an equal amount of money." Brenda responds, "That may be true, but if you give me $7, I will be $1 short of having twice as much money as you." How much money did John and Brenda have?
Hint: When one person loses $7, the other person gains $7.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! John says to Brenda, "If you give me $7, we will have an equal amount of money." Brenda responds, "That may be true, but if you give me $7, I will be $1 short of having twice as much money as you." How much money did John and Brenda have?
:
Let j = amt that John has
Let b = amt that Brenda has
;
Step-by-step
J says to B,"If you give me $7, we will have an equal amount of money."
j + 7 = b - 7
j = b - 7 - 7
j = (b - 14)
;
B says, "if you give me $7, I will be $1 short of having twice as much money as you."
b + 7 = 2(j-7) - 1
b + 7 = 2j - 14 - 1
b + 7 = 2j - 15
b = 2j - 15 - 7
b = 2j - 22
:
How much money did John and Brenda have?
From the 1st statement replace j with(b-14) in the above equation
b = 2(b-14) - 22
b = 2b - 28 - 22
b = 2b - 50
+50 = 2b - b
b = $50 is Brenda's amt
Find j
j = b - 14
j = 50 - 14
j = $36 is John's amt
;
:
Check this in both statements
J says to B,"If you give me $7, we will have an equal amount of money."
36 + 7 = 50 - 7
43 = 43
and
B says, "if you give me $7, I will be $1 short of having twice as much money"
50 + 7 = 2(36-7) - 1
57 = 2(29) - 1
57 = 58 - 1
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