Question 219001: Tim had $5.03 in quarters, nickels, dimes, pennies, and half-dollars in a desk drawer. He has five more nickels than quarters, the number of pennies is two-thirds the number of nickles, there are half as many dimes as nickels.How many coins of each type does he have?
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! Let  = number of quarters he has
Let  = number of dimes he has
Let  = number of nickels he has
Let  = number of pennies he has
Let  = number of half-dollars he has
Just by looking at the amount of money Tim has,
you can tell a lot about the coins that make it up.
(1) The number of half dollars must be less than
 , since that would leave no room for other coins
(2) He must have at least 3 pennies to get $5.53.
-----------------------------------------------------
given:
(1)
(2)
(3)
(4) (in pennies)
-----------------------------------------
There are  unknowns and only  equations, so
it will take some extra work to get the answer
From (1), 
Substituting into (4),
Multiply both sides by 
I need a combination of and that
will give me  , and must be  or less
--------------------
There can't be half-dollars,
I'll try  halfs
Can't be it, increasing takes me over
Next increase in takes me over
not it
not it
 BINGO
Now I know that
and
and
and
Tim has 8 pennies, 12 nickels, 6 dimes, 7 quarters, and 4 half-dollars
check answer:
(4)
OK
|
|
|
