An online electronics store must sell at least $2,500 worth of printers and monitors per day. Each printer costs $125 and each monitor costs $225 and each monitors costs $125. The store can ship a maximum of 15 items per day. What is the maximum number of printers it can ship each day?

Answer

To solve the problem step by step, we will define the variables and set up the inequalities based on the conditions provided.

### Step 1: Define the Variables
Let:
- \( p \) = number of printers sold each day
- \( m \) = number of monitors sold each day

### Step 2: Set Up the Inequalities
1. The store can ship a maximum of 15 items per day:
\[ p + m \leq 15 \]

2. The store must sell at least $2,500 worth of printers and monitors per day. The cost of each printer is $125 and each monitor is $225:
\[ 125p + 225m \geq 2500 \]

### Step 3: Simplify the Second Inequality
We can simplify the second inequality:
\[ 125p + 225m \geq 2500 \]
Dividing the entire inequality by 25 gives:
\[ 5p + 9m \geq 100 \]

### Step 4: Solve the System of Inequalities
Now we have the system of inequalities:
1. \( p + m \leq 15 \)
2. \( 5p + 9m \geq 100 \)

To maximize the number of printers \( p \), we can express \( m \) in terms of \( p \) from the first inequality:
\[ m = 15 - p \]

### Step 5: Substitute into the Second Inequality
Substituting \( m \) in the second inequality:
\[ 5p + 9(15 - p) \geq 100 \]
Expanding this gives:
\[ 5p + 135 - 9p \geq 100 \]
Combining like terms:
\[ -4p + 135 \geq 100 \]
Subtracting 135 from both sides:
\[ -4p \geq -35 \]
Dividing by -4 (and flipping the inequality sign):
\[ p \leq 8.75 \]

### Step 6: Determine the Maximum Whole Number of Printers
Since \( p \) must be a whole number, the maximum value for \( p \) is 8.

### Step 7: Verify the Solution
If \( p = 8 \), then:
\[ m = 15 - 8 = 7 \]
Now, check if this satisfies the second inequality:
\[ 5(8) + 9(7) = 40 + 63 = 103 \geq 100 \]
This condition is satisfied.

### Conclusion
The maximum number of printers that can be shipped each day is:
\[ \boxed{8} \]