4 pens and 6 pencils cost Rs 172. 2 pens and 2 pencils cost Rs 74. Find the cost of 1 pencil. 

We are given the following information:

1. The cost of 4 pens and 6 pencils is Rs 172.
2. The cost of 2 pens and 2 pencils is Rs 74.

Let the cost of 1 pen be \( x \) and the cost of 1 pencil be \( y \).

From the information given, we can form two equations:

1. \( 4x + 6y = 172 \)  (Equation 1)
2. \( 2x + 2y = 74 \)  (Equation 2)

### Solving the system of equations:
First, simplify Equation 2 by dividing through by 2:

\[
x + y = 37  \quad \text{(Equation 3)}
\]

Now, substitute \( x = 37 - y \) from Equation 3 into Equation 1:

\[
4(37 - y) + 6y = 172
\]

Expanding this equation:

\[
148 - 4y + 6y = 172
\]

Simplify:

\[
148 + 2y = 172
\]

Now, subtract 148 from both sides:

\[
2y = 24
\]

Solve for \( y \):

\[
y = \frac{24}{2} = 12
\]

Thus, the cost of 1 pencil is Rs 12.

Would you like further details or have any questions?

Here are 5 related questions to expand on this:
1. What is the cost of one pen?
2. How do you solve linear equations with two variables?
3. Can you solve for the total cost of 3 pens and 5 pencils now?
4. What is the graphical representation of these equations?
5. How do substitution and elimination methods compare in solving such problems?

**Tip:** When solving simultaneous equations, substitution is often simpler when one variable can easily be isolated from one of the equations.

4 pens and 6 pencils cost Rs 172. 2 pens and 2 pencils cost Rs 74. Find the cost of 1 pencil.

Discover how to determine the cost of one pencil given the cost equations for multiple pens and pencils. This problem involves solving linear equations and is suitable for students in Grades 7-9. Learn step-by-step methods to isolate variables and find solutions.

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