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The image shows a word problem where a teacher purchases calculators and measuring tapes for her class. The system of equations in the image is:

1. $ 20c + 10m = 495 $
2. $ 8c + m = 178.50 $

Here, $ c $ represents the cost of one calculator, and $ m $ represents the cost of one measuring tape.

### Interpretation of the equations:

1. **First Equation:**
   - $ 20c + 10m = 495 $
   - This equation represents the initial purchase the teacher made: 20 calculators and 10 measuring tapes for a total cost of $495. 
   - The solution to this equation gives the relationship between the price of each calculator and each measuring tape for this first purchase.

2. **Second Equation:**
   - $ 8c + m = 178.50 $
   - This equation represents the second purchase the teacher made, which includes 8 calculators and 1 measuring tape for a total cost of $178.50.
   - The solution to this equation gives the relationship between the cost of 8 calculators and 1 measuring tape for this second purchase.

### Next steps:

To find the exact values of $ c $ and $ m $, we can solve this system of linear equations.

Would you like me to solve the system of equations, or do you have any other specific questions about this problem?

Here are five follow-up questions you might consider:
1. How can you solve the system of equations using substitution?
2. How can you solve the system of equations using elimination?
3. What does the solution of this system represent in terms of real-world values?
4. What happens if the prices of calculators and measuring tapes change?
5. How does the second order affect the total budget the teacher planned?

**Tip:** When solving systems of equations, it's often useful to use substitution or elimination methods for efficiency.

A teacher purchased 20 calculators and 10 measuring tapes for her class and paid $495. Later, she realized she needed more supplies and ordered 8 calculators and 1 measuring tape, paying $178.50. The system of equations describing the purchases is: 20c + 10m = 495 and 8c + m = 178.50. What do the solutions to each equation represent?

Explore how to solve a real-world problem involving systems of linear equations. Learn how a teacher’s purchase of calculators and measuring tapes leads to two equations: 20c + 10m = 495 and 8c + m = 178.50. Discover how to find the cost of each item using algebraic methods like substitution or elimination. Suitable for students in Grades 8-10.

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