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) About Me  (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
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Cheers,
Stan H.
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of nuts Charlotte has initially
Let +b+ = number of nuts Lydia has initially
---------------------
(1) +a%2Fb+=+6%2F7+
(2) +%28+a+-+36+%29+%2F+%28+b+%2B+36+%29+=+9%2F17+
--------------------------------
(1) +a+=+%286%2F7%29%2Ab+
and
(2) +a+-+36+=+%289%2F17%29%2A%28+b+%2B+36+%29+
Substitute (1) into (2)
(2) +%286%2F7%29%2Ab+-+36+=+%289%2F17%29%2A%28+b+%2B+36+%29+
Multiply both sides by +17%2F9+
(2) +%28+34%2F21+%29%2Ab+-+68+=+b+%2B+36+
(2) +%28+34%2F21+%29%2Ab+-+b+=+104+
(2) +%28+13%2F21+%29%2Ab+=+104+
(2) +b+=+%28+21%2F13+%29%2A104+
(2) +b+=+168+
and
(1) +a+=+%286%2F7%29%2Ab+
(1) +a+=+%286%2F7%29%2A168+
(1) +a+=+144+
---------------------
Lydia has 168 nuts at first
----------------------------
check:
(1) +a%2Fb+=+6%2F7+
(1) +144%2F168+=+6%2F7+
(1) +.8571429+=+.8571429+
and
(2) +%28+a+-+36+%29+%2F+%28+b+%2B+36+%29+=+9%2F17+
(2) +%28+144+-+36+%29+%2F+%28+168+%2B+36+%29+=+9%2F17+
(2) +108+%2F+204+=+9%2F17+
(2) +5294118+=+.5294118+
OK

Answer by MathTherapy(10551) About Me  (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: %286x+-+36%29%2F%287x+%2B+36%29+=+9%2F17

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

102x – 612 = 63x + 324

102x – 63x = 324 + 612

39x = 936

x, or multiplicative factor = 936%2F39+=+24

Number of nuts Lydia had, initially: 7(24), or highlight_green%28168%29