Question 1202336
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Answer: <font color=red size=4>$64</font>



Work Shown:


H = Helen's amount
A = Alice's amount
T = Tom's amount
S = Sally's amount


Let's list what info we're given
<table border = "1" cellpadding = "5"><tr><td>Fact 1</td><td>Tom, Alice, Helen and Sally had $430 altogether. </td></tr><tr><td>Fact 2</td><td>Alice and Helen had the same amount of money. </td></tr><tr><td>Fact 3</td><td>Alice had 2/3 of the amount Tom had left after he had spent $86. </td></tr><tr><td>Fact 4</td><td>Sally was given $16 and she had as much as Alice. </td></tr></table>
Those facts lead to these four equations
H+A+T+S = 430  due to fact 1
A = H because of fact 2
A = (2/3)*(T-86) because of fact 3
S+16 = A because of fact 4


I'll label those equation (1) through equation (4).


Solve equation (3) for T
A = (2/3)*(T-86)
3A = 2(T-86)
3A = 2T-172
3A+172 = 2T
2T = 3A+172
T = (3A+172)/2
T = 1.5A+86


Then we'll plug in A = S+16
T = 1.5A+86
T = 1.5(S+16)+86
T = 1.5S+24+86
T = 1.5S+110


Let's move to equation (1)
H+A+T+S = 430 
A+A+T+S = 430  ... plug in A = H
2A+T+S = 430 
2(S+16)+T+S = 430 ... plug in A = S+16
2S+32+T+S = 430 
3S+32+T = 430 
3S+32+1.5S+110 = 430 ... plug in T = 1.5s+110 
4.5S+142 = 430 
4.5S = 430-142 
4.5S = 288 
S = 288/4.5 
S = <font color=red>64</font>
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