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?
+128408 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
