Question 1202336
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Tom, Alice, Helen and Sally had $430 altogether. Alice and Helen had the same amount of money. Alice had 2/3 of the amount Tom had left after he had spent $86. Sally was given $16 and she had as much as Alice. How much money did Sally have at first?

Let amount Sally had, be S    
Then Alice had: S + 16     
Since Helen and Alice had the same amount, then Helen’s was also S + 16
Since total amount was $430, Tom then had: 430 - (S + S + 16 + S + 16) = 430 - (3S + 32) = 430 - 3S - 32 = 398 - 3S 
After spending $86, Tom then had remaining amount of, 398 - 3S - 86 = 312 - 3S
Since Alice had 2/3 of Tom’s, after Tom spent $86, we then get: {{{matrix(3,3, S + 16, "=", (2/3)(312  -  3S), S + 16, "=", (2/3)3(104  -  S), 
S + 16, "=", (2/cross(3))cross(3)(104 - S))}}} 
                                                                S + 16 = 2(104 - S)
                                                                S + 16 = 208 - 2S
                                                                S + 2S = 208 - 16
                                                                    3S = 192
                                       Initial amount Sally had, or {{{highlight_green(matrix(1,5, S, "=", 192/3, "=", highlight("$64")))}}}</pre>