If Val currently has 20 nickels and finds twice as many nickels as she has in her older brother's treasure box, she will have 2*20=40 more nickels.
The total number of nickels she'll have is 40+20=<<40+20=60>>60
Since nickel is worth $0.05, the value of the nickels Val is having is 60*0.05=$<<60*0.05=3>>3
Val had three times as many dimes as nickels before she found the 40 new nickels, a total of 3*20=<<3*20=60>>60 dimes
Since a dime has a value of $0.10, the value of the dimes that Val has is 60*$0.10=$<<60*0.10=6>>6
Together, the value of the dimes and nickels Val has is worth $6+$3=$<<6+3=9>>9
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