Question

A piggy bank contains $2.10 in nickels and quarters. The number of nickels is 2 more than 3 times the number of quarters. How many nickels are there? What is their total value?

Answer 1

To solve the problem, we used algebra to set up two equations representing the known information, and then we solved for the number of nickels, which is 17, with a total value of $0.85.

Step-by-step explanation:

The student asked how many nickels are in a piggy bank given that there are $2.10 in nickels and quarters, and the number of nickels is 2 more than 3 times the number of quarters. To solve this, we set up two equations.

Let N be the number of nickels and Q be the number of quarters. We know that:

• Each nickel is worth $0.05, and each quarter is worth $0.25.
• The total value of the coins is $2.10.
• The number of nickels (N) is 2 more than 3 times the number of quarters (Q) which gives us N = 3Q + 2.

Our equations are:

1. 0.05N + 0.25Q = $2.10
2. N = 3Q + 2

Substituting the second equation into the first gives us:

• 0.05(3Q + 2) + 0.25Q = $2.10
• 0.15Q + 0.10 + 0.25Q = $2.10
• 0.40Q + 0.10 = $2.10
• 0.40Q = $2.00
• Q = $2.00 / 0.40
• Q = 5 quarters

Substitute Q back into N = 3Q + 2 to get:

• N = 3(5) + 2
• N = 15 + 2
• N = 17 nickels

The total value of the nickels is 17 nickels x $0.05/nickel, which is $0.85.

Therefore, there are 17 nickels with a total value of $0.85.