Let $n$ represent the number of nickels and $d$ represent the number of dimes. We can set up a system of equations based on the information provided:

1. Total Coin Count Equation: Latanya has 24 nickels and dimes combined. $n + d = 24$

2. Total Value Equation: The total value of the nickels and dimes is $1.90. Since nickels are worth 5 cents and dimes are worth 10 cents, we have: $0.05n + 0.10d = 1.90$

To simplify calculations, we can multiply the second equation by 100 to eliminate the decimals: $5n + 10d = 190$

Now we have the system of equations: $n + d = 24$ $5n + 10d = 190$

Step 1: Simplify the System

We can simplify the second equation by dividing by 5: $n + d = 24$ $n + 2d = 38$

Step 2: Solve the System by Elimination

Subtract the first equation from the second: $(n + 2d) - (n + d) = 38 - 24$ $d = 14$

Step 3: Substitute $d = 14$ into the First Equation

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

Conclusion

Latanya has:

• $n = 10$ nickels
• $d = 14$ dimes

Would you like more details or have questions about the solution? Here are some related questions for practice:

1. What if Latanya had $2.40 instead of $1.90?
2. If Latanya had twice as many dimes as nickels, how would the equations change?
3. How many nickels and dimes would she have if the total was 20 coins instead of 24?
4. What if the total value was $2.10 with 24 coins—how would this affect the solution?
5. How would the approach differ if pennies were included?

Tip: Always try to simplify equations by eliminating decimals first to make calculations easier.