Let's solve this step-by-step.

Let:

• $n$ represent the number of nickels.
• $d$ represent the number of dimes.

Given:

1. The total number of coins (nickels and dimes) is 24: $n + d = 24$
2. The total value of the coins is $1.90, or 190 cents: $5n + 10d = 190$

Now, let's solve these equations.

Step 1: Simplify the second equation

We can divide the second equation by 5 to make it easier: $n + 2d = 38$

Step 2: Set up a system of equations

Now we have:

1. $n + d = 24$
2. $n + 2d = 38$

Step 3: Subtract the first equation from the second

Subtracting $n + d = 24$ from $n + 2d = 38$: $(n + 2d) - (n + d) = 38 - 24$ $d = 14$

Step 4: Substitute $d = 14$ back into the first equation

$n + 14 = 24$ $n = 10$

Solution

Latanya has:

• 10 nickels
• 14 dimes

Would you like further details or have any questions?

Here are five related questions for further exploration:

1. What if Latanya had a different total value, like $2.00, with 24 coins?
2. How would you solve if she had 30 coins worth $1.80?
3. What if the total number of coins was unknown?
4. How would you set up the equation if she had quarters and dimes instead?
5. What other ways could you approach this system of equations?

Tip: Always check your solution by plugging values back into the original equations to verify.