Math Snap

STEP 1

What is this asking?
How many nickels and dimes does Kevin have if he has $\$4.85$ total, and $34$ fewer dimes than nickels?
Watch out!
Don't mix up the values of nickels ($5$ cents) and dimes ($10$ cents)!

STEP 2

1. Set up variables and equation
2. Solve for the number of nickels
3. Solve for the number of dimes
4. Calculate the total number of coins

STEP 3

Let $n$ be the number of nickels and $d$ be the number of dimes.
We know a nickel is worth $\$0.05$, and a dime is worth $\$0.10$.

STEP 4

We're told Kevin has $\$4.85$ in total.
We can write this as an equation:
$$0.05n + 0.10d = 4.85$$ This equation represents the total value of his coins.

STEP 5

We also know he has $34$ fewer dimes than nickels.
Mathematically, this means:
$$d = n - 34$$ This equation relates the number of nickels and dimes.

STEP 6

Now, let's substitute the second equation into the first equation.
This way, we get an equation with only one variable, $n$:
$$0.05n + 0.10(n - 34) = 4.85$$

STEP 7

Distribute the $0.10$:
$$0.05n + 0.10n - 3.40 = 4.85$$

STEP 8

Combine the $n$ terms:
$$0.15n - 3.40 = 4.85$$

STEP 9

Add $3.40$ to both sides of the equation:
$$0.15n = 4.85 + 3.40$$ $$0.15n = 8.25$$

STEP 10

Divide both sides by $0.15$ to find $n$:
$$n = \frac{8.25}{0.15}$$ $$n = 55$$So, Kevin has $55$ nickels!

STEP 11

We know $d = n - 34$, and we just found that $n = 55$.
Let's substitute $n = 55$ into this equation:
$$d = 55 - 34$$ $$d = 21$$Kevin has $21$ dimes!

STEP 12

To find the total number of coins, we simply add the number of nickels and dimes:
$$55 + 21 = 76$$

Kevin has a total of $\textbf{76}$ coins.
So the correct answer is C.