+0  
 
0
26
1
avatar

A jar of change has $16.45 in it. There are 6 fewer nickels than half the dimes and 8
fewer quarters than 1⁄4 the amount of dimes. How many of each coin is in the jar?

 Apr 20, 2021
 #1
avatar+118505 
+1

Let  the  number of dimes =  D

Then the  number of nickels= (1/2  D - 6)

And  the  number  of quarters  = (1/4 D  - 8)

 

So

 

Value of a dime * number  +  value of a nickel * number +  value of a quater * number =  16.45

 

Putting the amounts into pennies  (to get rd of  the decimals)  we  have

 

10D  +  5 [ (1/2)D - 6 ]  + 25 [ (1/4)D - 8 ]  = 1645

 

10D   +  (5/2)D   -  30  + (25/4)D  - 200  = 1645

 

(40/4)D  + (10/4)D  + (25/4)D  = 1645  + 30  + 200

 

(75/4)D  =  1875

 

D = 1875  ( 4/75)   =  100  dimes

 

And

 

(1/2)(100)  -6  =   44  nickels

 

And

 

(1/4)(100)  - 8   =  17  quarters

 

 

cool cool cool

 Apr 20, 2021

22 Online Users

avatar