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Students are donating money to a charity fund that helps less privileged kids. The number of $2, $5 and $10-notes donated are in the ratio of 7 : 2 : 3. 5 7 of the $2-notes and 9 $5-notes are taken out. The remaining notes are worth $307. How many $10-notes are there?

 May 16, 2023
 #1
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Let the initial number of $2, $5 and $10-notes be 7x, 2x and 3x respectively. After 5/7 of the $2-notes and 9 $5-notes are taken out, the number of remaining $2-notes and $5-notes are 2x and 3x-9 respectively. The total value of the remaining notes is 2x2 + (3x-9)5 + 3x10 = 307 11x = 262 x = 24 Therefore, the number of $10-notes is 3x = 3*24 = 72. So the answer is 72

 May 16, 2023
 #2
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T==Two-dollar bills,  F==Five-dollar bills,  N==Ten-dollar bills

 

T / F ==7/2............................................(1)  

T/N=7/3................................................(2)   

F/N==2/3..............................................(3)  

2*(2/7T) + 5*(F - 9) + 10N==307.........(4), solve for T, F, N

 

T==56 - 2-dollar bills before withdrawal of 5/7 of them

F==16 - 5-dollar bills before withdrawal of 9 of them

N==24 - 10-dollar bills.

 May 16, 2023

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