Brenda has saved 300 coins, consisting of 25 centavo and 10 centavo coins. If the total value of her Savings is 45 pesos, how many 10 centavo coins did she save

Let the number of 25 centavo coins Brenda has be \( x \), and the number of 10 centavo coins be \( y \). We know the following information:

1. **Total number of coins**: 
   \[
   x + y = 300
   \]
2. **Total value of the coins**: Since the value of 25 centavo coins is \( 0.25 \) pesos and the value of 10 centavo coins is \( 0.10 \) pesos, we can express the total value equation in pesos as:
   \[
   0.25x + 0.10y = 45
   \]

### Step 1: Solve for one variable
From the first equation, solve for \( x \):
\[
x = 300 - y
\]

### Step 2: Substitute into the value equation
Substitute \( x = 300 - y \) into the second equation:
\[
0.25(300 - y) + 0.10y = 45
\]

### Step 3: Simplify the equation
\[
0.25(300) - 0.25y + 0.10y = 45
\]
\[
75 - 0.25y + 0.10y = 45
\]
\[
75 - 0.15y = 45
\]

### Step 4: Solve for \( y \)
Subtract 75 from both sides:
\[
-0.15y = 45 - 75
\]
\[
-0.15y = -30
\]
Now, divide both sides by \( -0.15 \):
\[
y = \frac{-30}{-0.15} = 200
\]

So, Brenda has saved **200** 10 centavo coins.

### Step 5: Verify the result
If \( y = 200 \), then from the first equation, \( x = 300 - 200 = 100 \). The total value should be:
\[
0.25(100) + 0.10(200) = 25 + 20 = 45
\]
The total value matches, confirming the solution is correct.

Brenda saved **200** 10 centavo coins.

Would you like further details on any step or have any questions?

Here are some related questions:
1. How many 25 centavo coins did Brenda save?
2. What would be the total value if Brenda saved 250 coins in total?
3. What is the value of all the 25 centavo coins she saved?
4. If Brenda had saved 100 pesos instead, how would the equation change?
5. How would the result change if Brenda saved a total of 400 coins?

**Tip**: When dealing with systems of equations, always aim to simplify one equation first and substitute values to reduce complexity.

Brenda has saved 300 coins, consisting of 25 centavo and 10 centavo coins. If the total value of her savings is 45 pesos, how many 10 centavo coins did she save?

Discover how to solve a system of linear equations to find out how many 10 centavo coins Brenda saved from her total of 300 coins, with a total value of 45 pesos. This step-by-step solution covers key algebraic concepts and is suitable for Grades 6-8 students.

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