72 coins nickels and dimes equal 4.95?

Answer 1

This is a simultaneous-equation problem. Because there are two variables - the number of nickels and the number of dimes - we have to set up two relationships between them in order to solve the system.

Let n be the number of nickels and d be the number of dimes.

Because there's a total of 72 coins, the first equation is n + d = 72.

The second thing we know is that the total value is $4.95. It's easiest to express each amount in cents, n nickels are worth 5n cents, d dimes are worth 10d cents, and $4.95 is 495 cents so the second equation is 5n + 10d = 495.

From here there are two ways to obtain the answer.

Method 1 - Substitution

1. Because the first equation is n + d = 72, we can express n in terms of n as n = 72 - d.
2. Then replace the "n" term of the second equation with the new expression in terms of d:

   5(72 - d) + 10d = 495

3. Expanding the left side gives 5*72 - 5d + 10d = 495.
4. Next collect like terms: 360 + 5d = 495
5. Finally solve for d: 5d = 495 - 360, or 5d = 135so d = 135/5, or d = 27; i.e. there are 27 dimes.
6. Because we know there are 72 coins in total (d + n = 72) there must be 45 nickels.

Method 2 - Balancing

1. Write the equations on two successive lines:

   n + d = 72

   5n + 10d = 495

2. The coefficient of n in the first equation is 1 (implied) and the coefficient in the second equation is 5 (explicit). To balance the two, multiply every term in the first equation by 5 so the "n" term has the same coefficient in both:

   5n + 5d = 360

   5n + 10d = 495

3. Both equations now share a "5n" term. The "d" coefficient is larger in the second equation so subtract the first equation from the second:

   5n + 10d = 495

   -[5n + 5d = 360]

   ------------------------

   or (5n - 5n) + (10d - 5d) = 495 - 360

4. The 5n and -5n terms cancel each other out, leaving 5d = 135, or d = 27 and n = 45, the same answer as in Method 1 (which it should be!!)

   Check: 27 dimes are worth 27*10 = $2.70. 45 nickels are worth 45*5 = $2.25. The total value is $4.95.

Answer 2

How much is 4 feet of nickels

Answer 3

45 nickles 27 dimes