Question

Jack has 14 coins consisting of nickels and dimes that total $0.90. How many nickels does Jack have?

• A. 10
• B. 8
• C. 4
• D. 6
• E. 12

Hint:

To avoid decimals, it's often easier to work with cents instead of dollars when solving coin problems. Just remember to convert the total value to cents as well ($0.90 = 90 cents).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a classic coin problem that can be solved with a system of linear equations. One equation represents the total number of coins, and the other represents their total value.
Step 2: Key Formula or Approach:
Let \(n\) be the number of nickels and \(d\) be the number of dimes. Equation for the number of coins: \[ n + d = 14 \] Equation for the value of the coins (in cents): \[ 5n + 10d = 90 \] We need to solve this system for \(n\).
Step 3: Detailed Explanation:
We can use the substitution method. From the first equation, express \(d\) in terms of \(n\): \[ d = 14 - n \] Now, substitute this into the second equation: \[ 5n + 10(14 - n) = 90 \] Distribute the 10: \[ 5n + 140 - 10n = 90 \] Combine the terms with \(n\): \[ -5n + 140 = 90 \] Subtract 140 from both sides: \[ -5n = 90 - 140 \] \[ -5n = -50 \] Divide by -5: \[ n = 10 \] Step 4: Final Answer:
Jack has 10 nickels.