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
<pre>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: {{{(6x - 36)/(7x + 36) = 9/17}}}
17(6x – 36) = 9(7x + 36) -------- Cross-multiplying
102x – 612 = 63x + 324
102x – 63x = 324 + 612
39x = 936
x, or multiplicative factor = {{{936/39 = 24}}}
Number of nuts Lydia had, initially: 7(24), or {{{highlight_green(168)}}}