Math Is Fun Forum

lbrewer

Member

Registered: 2007-03-17

Posts: 1

algebra

A student counting his change arranges 30 pennies in a line. He then replaces every second penny with a nickel. He continues by replacing every thrid coin with a dime, every fourth coin with a quarter, every fifth with a half dollar,  and every sixth coin with a dollar. What is the total value of the money in the line when he is finished? Can anybody show me how to work this in detail?
Thanks

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: algebra

Coins 6, 12, 18, 24, 30 will be replaced by dollars (100).
Coins 5, 10, 15, 20, 25 will be replaced by half-dollars (50).
Coins 4, 8, 16, 28 will be replaced by quarters (25).
Coins 3, 9, 21, 27 will be replaced by dimes (10).
Coins 2, 14, 22, 26 will be replaced by nickels (5).
The rest (1, 7, 11, 13, 17, 19, 23, 29) will remain pennies (1).

∴ Total value in cents = 5×100 + 5×50 + 4×25 + 4×10 + 4×5 + 8×1 = 500 + 250 + 100 + 40 + 20 + 8 = 918, i.e. he has $9.18.

Last edited by JaneFairfax (2007-03-17 03:34:38)