Coins Question!

Question

In a cash register there are nickels, dimes, and quarters. One half the coins are nickels, one fifth are dimes, and the rest are quarters. If the total value is $6.00, how many coins of each type are there in the register?

Answer 1

If x is the total number of coins, then...

0.5x ($0.05) + 0.2x ($0.10) + 0.3x ($0.25) = $6.00

$0.025x + $0.02x + $0.075x = $6.00

$0.12x = $6.00

x = 50

Thus, 50 coins in all --> 25 nickels ($1.25), 10 dimes ($1.00), & 15 quarters ($3.75)

Answer 2

Fun Question! We are solving for the total number of coins. Let's call our unknown C, for Coins.

First we need to figure out what fraction of the coins are quarters.

If half of the coins are nickels, and one fifth are dimes, then 1 - 1/2- 1/5 are quarters.

When we add and subtract fractions, we need a common denominator; for this problem the common denomminator is 10. 1=10/10, 1/2 = 5/10 and 1/5 = 2/10. 10/10- 5/10-2/10 =3/10., so 3/10's of the coins are quarters. Of course a nickel is worth 5 cents, a dime is worth 10 cents, and a quarter is worth 25 cents,

The number of nickels is 1/2 C, worth 0.05*1/2C

The number of dimes is 1/5 C, worth 0.10*1/5C

The number of quarters is 3/10 C , worth 0.25* 3/10C

The total value of ll the coins is $6

We are now ready to set u our equation to solve.

This is a little weird because we have fractions and decimals, but that's okay. Remember a fraction bar is simply a division symbol.

0.05*1/2C+0.10*1/5C+0.25*3/10C=6.00

0.025C+.02C+0.075C=6.00

0.12C=6

C=50

There are 50 coins in the cash register.