Stella has 63 coins .The coins are a mixture of quarters and dimes . She has a total of How many quarters and how many dimes does Stella have?

Question

Equation 1: __ Equation 2:
__
Stella has __ quarters and __ dimes.

Answer 1

To determine the number of quarters and dimes Stella has, we need to set up a system of equations based on the information given.

1. Let's use:
- \( q \) to represent the number of quarters.
- \( d \) to represent the number of dimes.

2. Given that Stella has a total of 63 coins, we can write this as:
*Equation 1:* \( q + d = 63 \)

3. Also given that the total value of these coins is $11.25, we can write this in terms of cents:
- The value of each quarter is 25 cents.
- The value of each dime is 10 cents.

Therefore, the total value equation can be:
*Equation 2:* \( 25q + 10d = 1125 \)

Now, we have a system of linear equations:

1. \( q + d = 63 \)
2. \( 25q + 10d = 1125 \)

Let's solve this system step-by-step.

**Step 1:** Simplify Equation 2 by dividing all terms by 5:
\[ 5q + 2d = 225 \]

**Step 2:** Now we have the simplified system:
\[ q + d = 63 \]
\[ 5q + 2d = 225 \]

**Step 3:** Solve Equation 1 for \( d \):
\[ d = 63 - q \]

**Step 4:** Substitute \( d = 63 - q \) into the simplified Equation 2:
\[ 5q + 2(63 - q) = 225 \]

**Step 5:** Distribute and combine like terms:
\[ 5q + 126 - 2q = 225 \]
\[ 3q + 126 = 225 \]

**Step 6:** Isolate \( q \):
\[ 3q = 225 - 126 \]
\[ 3q = 99 \]
\[ q = 33 \]

So, Stella has 33 quarters.

**Step 7:** Substitute \( q = 33 \) back into Equation 1 to find \( d \):
\[ 33 + d = 63 \]
\[ d = 63 - 33 \]
\[ d = 30 \]

**Conclusion:**
Stella has 33 quarters and 30 dimes.

Therefore, the equations and the solution are:
Equation 1: \( q + d = 63 \)
Equation 2: \( 25q + 10d = 1125 \)

Stella has 33 quarters and 30 dimes.