Question

Harold has a total of 17 coins that are nickels

and pennies. The value of the coins is $0.41.
How many nickels and pennies are there?

Answer 1

Let's denote the number of nickels as "n" and the number of pennies as "p". We can set up a system of two equations to represent the given information:

n + p = 17 (equation 1 - total number of coins)
0.05n + 0.01p = 0.41 (equation 2 - total value of coins in dollars)

To solve for n and p, we can use the method of substitution. Solve equation 1 for n:

n = 17 - p

Substitute this expression for n into equation 2 and solve for p:

0.05(17 - p) + 0.01p = 0.41

0.85 - 0.05p + 0.01p = 0.41

-0.04p = -0.44

p = 11

Substitute this value for p into equation 1 to solve for n:

n + 11 = 17

n = 6

Therefore, there are 6 nickels and 11 pennies.

Answer 2

2 nickels and 15 pennies

Explanation:

Let’s use n to represent the number of nickels and p to represent the number of pennies. We know that Harold has a total of 17 coins, so we can write:

n + p = 17

We also know that the value of the coins is $0.41. Since a nickel is worth $0.05 and a penny is worth $0.01, we can write:

0.05n + 0.01p = 0.41

Now we have two equations with two variables. We can solve for n and p using substitution or elimination.

Let’s use substitution. Solve for n in the first equation:

n = 17 - p

Substitute this expression for n in the second equation:

0.05(17 - p) + 0.01p = 0.41

Simplify and solve for p:

0.85 - 0.04p + 0.01p = 0.41

-0.03p = -0.44

p = 14.67

Since we can’t have a fraction of a penny, we’ll round up to 15 pennies.

Now we can solve for n using the first equation:

n + 15 = 17

n = 2

So Harold has 2 nickels and 15 pennies.