Two machines, P and Q, produce 100 toys in 2 hours. In 6 hours, machine P produces 48 more toys than machine Q. How many toys does machine P produce in 1 hour? 

Let's define the variables to solve the problem:

- Let \( P \) be the number of toys machine P produces per hour.
- Let \( Q \) be the number of toys machine Q produces per hour.

### Step 1: Set up the first equation.
In 2 hours, both machines together produce 100 toys. So:

\[
2P + 2Q = 100
\]

Dividing the entire equation by 2:

\[
P + Q = 50 \quad \text{(Equation 1)}
\]

### Step 2: Set up the second equation.
In 6 hours, machine P produces 48 more toys than machine Q. Therefore:

\[
6P = 6Q + 48
\]

Dividing the entire equation by 6:

\[
P = Q + 8 \quad \text{(Equation 2)}
\]

### Step 3: Solve the system of equations.
Now, substitute Equation 2 into Equation 1:

\[
(Q + 8) + Q = 50
\]

Simplifying:

\[
2Q + 8 = 50
\]

Subtract 8 from both sides:

\[
2Q = 42
\]

Divide by 2:

\[
Q = 21
\]

Now, substitute \( Q = 21 \) into Equation 2:

\[
P = 21 + 8
\]

\[
P = 29
\]

### Final Answer:
Machine P produces **29 toys per hour**.

Would you like any further details or have any questions? Here are some related questions:

1. How many toys does machine Q produce in 1 hour?
2. How many toys does machine P produce in 5 hours?
3. How many toys do machines P and Q produce together in 4 hours?
4. What if machine P produced 60 more toys than machine Q in 6 hours? How would the answer change?
5. How would the total production change if the efficiency of both machines increased by 20%?

**Tip:** Always double-check your equations by substituting values back into the original conditions of the problem.

Two machines, P and Q, produce 100 toys in 2 hours. In 6 hours, machine P produces 48 more toys than machine Q. How many toys does machine P produce in 1 hour?

Discover how to solve a problem involving two machines producing toys using a system of linear equations. This step-by-step guide explains how to determine the number of toys machine P produces per hour, ideal for students in Grades 8-10.

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