Answer:
Let n = the number of nickels
Let d = the number of dimes
Let q = the number of quarters
The value of the coins is $5.50:
The number of nickels is three times that of the dimes:
The number of nickels is six more than twice the number of quarters:
Putting this together in a system we get:
Simplifying the system we get:
Eliminating n from equations (1b) and
(2b) we get:
Eliminating n from equations (2b) and
(3b) we get:
Putting equations (4) and (5) together into a system of two equations
and two unknowns we get:
Eliminating d from equations (4) and
(5) we get:
Solving for q we get:
Plugging in 12 for q in equation (3)
and solving for n we get:
Plugging in 30 for n in equation (2)
we get:
There are 30 nickels, 10 dimes and 12 quarters. |