Question 1199590
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A = number of coins in box A
B = number of coins in box B
C = number of coins in box C


Stated facts:
<ol><li><font color="blue">A has 5 times as many coins as C.</font></li><li><font color="blue">B has 12 fewer than A.</font></li><li><font color="blue">C has half the number in B</font></li></ol>Let's translate each of those three statements into symbolic form.<ul><li>A = 5C  from fact 1</li><li>B = A-12 from fact 2</li><li>C = 0.5B from fact 3</li></ul>Then apply a combination of fact 1 and fact 3.
A = 5C
A = 5*0.5B
A = 2.5B


Now involve fact 2 so we can solve for B.
B = A-12
B = 2.5B-12
B-2.5B = -12
-1.5B = -12
B = -12/(-1.5)
B = 8
There are 8 coins worth 50 cents each in box B.


Then,
A = 2.5B
A = 2.5*8
A = 20
There are 20 coins worth $1 each from box A.
Ultimately we have 20*1 = 20 dollars in box A.



Answer: <font color=red>$20</font>
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