The 24 Coins
3) There are 24 coins that total $2.90 -- nickels, dimes, and
quarters. There are 4 more dimes than quarters. How many of
each of these coins is there?
25x + 10(x + 4) + 5(20 -2x) = 290
25x + 10x +40 + 100 -10x = 290
25x + 140 = 290
25x = 150
x = 6
Since "x" is 6, then there are 6 quarters, (6 + 4) dimes,
and (20-12) nickels.
1.50 (6 quarters)
1.00 (10 dimes)
0.40 (8 nickels)
-------------------------
2.90 (24 coins)
As you can see in the formula above, the term for the dime
takes the number value of "x" and adds 4 to it (since there are
4 more dimes than nickels). The term for the nickel includes
"20-2x." Though there are 24 coins, we subtract the 4 that are
being "reserved" for the dimes, to come up with this number in
the formula. The "-2x" will then deduct the amount of the quarters
and dimes from the nickels.