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A box contains 81 coins, only dimes and nickels. The amount of money in the box is $5.30. How many dimes and how many nickels are in the box?

 Mar 16, 2020
 #1
avatar+29984 
+2

"A box contains 81 coins, only dimes and nickels. The amount of money in the box is $5.30. How many dimes and how many nickels are in the box?"

 

d + n = 81   (1)

10d + 5n = 530 divide by 5 to get 2d + n = 106   (2)

 

Subtract (1) from (2):   d = 106 - 81 = 25   (3)

 

Use (3) in (1):  25 + n = 81 or n = 81 - 25 = 56

 

There are 25 dimes and 56 nickels.

 Mar 16, 2020
 #2
avatar+23553 
+1

x = nickels           value    = 5x

(81-x) = dimes     value =  10 (81-x)         summed, the values = 530

 

5x + 10(81-x) = 530     solve for 'x' ..the number of nickels   then dimes =   81-x

 Mar 16, 2020

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