SOLUTION: Hi Charlotte and Lydia shared cashew nuts in the ratio of 6:7.when Charlotte gave 36 nuts to Lydia the ratio of nuts Charlotte has to lydia is 9:17.how many nuts did Lydia have at

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Question 1033494: Hi
Charlotte and Lydia shared cashew nuts in the ratio of 6:7.when Charlotte gave 36 nuts to Lydia the ratio of nuts Charlotte has to lydia is 9:17.how many nuts did Lydia have at first.
thank you
Found 3 solutions by stanbon, josmiceli, MathTherapy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Charlotte and Lydia shared cashew nuts in the ratio of 6:7.when Charlotte gave 36 nuts to Lydia the ratio of nuts Charlotte has to lydia is 9:17.how many nuts did Lydia have at first.
----
Start::
Charlotte had 6x nuts
Lydia had 7x nuts
-----
After the exchange::
Charlotte had 6x-36 nuts
Lydia had 7x+36
-----
Equation:
6x-36/7x+36 = 9/17
-----
17(6x-36) = 9(7x+36)
102x - 17*36 = 63x + 9*36
--------
39x = 26*36
--------
13x = 26*12
x = 2*12 = 24
----
Ans: Charlotte had 6x = 6*24 = 144 nuts
Lydia had 7x = 7*24 = 140+28 = 168 nuts
-------------------
Cheers,
Stan H.
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Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = number of nuts Charlotte has initially
Let = number of nuts Lydia has initially
---------------------
(1)
(2)
--------------------------------
(1)
and
(2)
Substitute (1) into (2)
(2)
Multiply both sides by
(2)
(2)
(2)
(2)
(2)
and
(1)
(1)
(1)
---------------------
Lydia has 168 nuts at first
----------------------------
check:
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
OK
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

Hi
Charlotte and Lydia shared cashew nuts in the ratio of 6:7.when Charlotte gave 36 nuts to Lydia the ratio of nuts Charlotte has to lydia is 9:17.how many nuts did Lydia have at first.
thank you
Let the multiplicative factor be x

Then initially Charlotte had 6x, and Lydia, 7x nuts

After Charlotte gave 36 nuts to Lydia, Charlotte had 6x – 36 left, and Lydia had: 7x + 36

We then get: 

17(6x – 36) = 9(7x + 36) -------- Cross-multiplying

102x – 612 = 63x + 324

102x – 63x = 324 + 612

39x = 936

x, or multiplicative factor = 

Number of nuts Lydia had, initially: 7(24), or  

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