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l0rrie
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Mrs. Anderson divided $420 evenly among her children. Later 03 Jun 2011, 11:27
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Mrs. Anderson divided $420 evenly among her children. Later, when Mrs. Anderson was away, Daniel, the eldest, took $5 from each of his brothers and sisters. Daniel ended up with $90. If Mrs. Anderson has more than 7 children, how many children does Mrs. Anderson have?

12
14
16
18
20


Here's what I did:

420/x + 5(x-1) = 90

However, I can't seem to solve for x.. Can somebody please help me :(



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LalaB
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Mrs. Anderson divided $420 evenly among her children. Later 03 Jun 2011, 11:39
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ANSW A

420/12 = 35 usd for each kid
Daniel- 5$*11 (12 kids less Daniel)+35 usd=90 usd


i.e.
5 (x-1)+ 420/x=90
x=12
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Mrs. Anderson divided $420 evenly among her children. Later 03 Jun 2011, 11:46
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Thanks.. I also tried plugging in numbers but I was wondering if someone here could explain the algebraic approach to me.. Thanks a lot
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Mrs. Anderson divided $420 evenly among her children. Later Updated on: 03 Jun 2011, 11:50
Originally posted by LalaB on 03 Jun 2011, 11:47.
Last edited by LalaB on 03 Jun 2011, 11:50, edited 1 time in total.
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l0rrie
Thanks.. I also tried plugging in numbers but I was wondering if someone here could explain the algebraic approach to me.. Thanks a lot
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5 (x-1)+ 420/x=90
x=12

p.s.-in my 1st post I actually tried to explain. to make it clear I began from the end ;) and then wrote the formula
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Mrs. Anderson divided $420 evenly among her children. Later 03 Jun 2011, 11:56
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I got the numbers right but I think I did something wrong in my calculation.. I can't solve for x I keep getting x is 4,4 when Im trying to solve this equation.. Could you please write it down for me how you solved for x is 12, thanks a bunch!
Here's what I got:

420/x + 5x = 95x
420 = 90x
x=4,4 :S
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Mrs. Anderson divided $420 evenly among her children. Later 03 Jun 2011, 11:58
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l0rrie
Mrs. Anderson divided $420 evenly among her children. Later, when Mrs. Anderson was away, Daniel, the eldest, took $5 from each of his brothers and sisters. Daniel ended up with $90. If Mrs. Anderson has more than 7 children, how many children does Mrs. Anderson have?

12
14
16
18
20


Here's what I did:

420/x + 5(x-1) = 90

However, I can't seem to solve for x.. Can somebody please help me :(
Show more

\(\frac{420}{x}+5(x-1)=90\)
\(\frac{420}{x}+5x-5=90\)
\(\frac{420+5x^2-5x}{x}=90\)
\(420+5x^2-5x=90x\)
\(5x^2-95x+420=0\)
Divide both sides by 5;
\(x^2-19x+84=0\)
\(x^2-12x-7x+84=0\)
\(x(x-12)-7(x-12)=0\)
\((x-7)(x-12)=0\)

x=7 OR x=12;
We know Mrs. Anderson has more than 7 children;
Thus, x=12.

Ans: "A"
*****************************************

PIN also works good for this.
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Mrs. Anderson divided $420 evenly among her children. Later 03 Jun 2011, 12:04
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Thanks so much fluke, that was exactly what I was looking for.. Why was my approach wrong.. I basically did:

420/x + 5x -5 = 90
420/x + 5x = 95 (multiplied both sides with x)
420 + 5x = 95x
420 = 90x

If you multiply by x that doesn't mean you have to do it for everything on the left side right, so in this case also the 5x? I always thought that you only need to multiply one 'one' part of either side..
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Mrs. Anderson divided $420 evenly among her children. Later 03 Jun 2011, 12:12
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l0rrie
Thanks so much fluke, that was exactly what I was looking for.. Why was my approach wrong.. I basically did:

420/x + 5x -5 = 90
420/x + 5x = 95 (multiplied both sides with x)
420 + 5x = 95x
420 = 90x

If you multiply by x that doesn't mean you have to do it for everything on the left side right, so in this case also the 5x? I always thought that you only need to multiply one 'one' part of either side..
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Any operation you do for LHS, you have to do it for RHS.
Also, the operation is not selective for multiplication/division. You have perform the operation for all terms for multiplication/division.

420/x + 5x = 95
Multiply both sides by x;

(420/x)*x+5x*x=95*x
420+5x^2=95x
Subtract 95x from both sides;
420+5x^2-95x=95x-95x
420+5x^2-95x=0
Rearrange:
5x^2-95x+420=0
Divide both sides by 5;
5x^2/5 - 95x/5 + 420/5 = 0/5
x^2-19x+84=0
*******************************
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Mrs. Anderson divided $420 evenly among her children. Later 03 Jun 2011, 12:22
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Again thanks, very clear now.. The rule you just described, is that only for multiplying/dividing?
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Mrs. Anderson divided $420 evenly among her children. Later 03 Jun 2011, 12:24
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Again thanks, very clear now.. The rule you just described, is that only for multiplying/dividing?
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Yes, that's only for "multiplication/division" thanks



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