Flour is sold in 5kg and 2kg packets. the 5 kg packets cost $2.75 each, and the 2 kg packets cost 1.25$ each. if the shop sells 67 kg of flour for a total of 38.50, how many of each size packet was sold? (find the system of equasions)

To solve the problem, we can set up a system of equations based on the information provided.

Let:
- $ x $ = number of 5 kg packets sold
- $ y $ = number of 2 kg packets sold

We have two pieces of information:

1. The total weight of flour sold is 67 kg:
   \[
   5x + 2y = 67
   \]

2. The total cost of flour sold is $38.50:
   \[
   2.75x + 1.25y = 38.50
   \]

Thus, the system of equations is:
1. $ 5x + 2y = 67 $
2. $ 2.75x + 1.25y = 38.50 $

Would you like to proceed with solving this system of equations, or do you have any specific questions about it? 

Here are some related questions you might consider:
1. How can we solve this system using substitution or elimination?
2. What would the graphical representation of these equations look like?
3. How would the solution change if the prices of the packets were different?
4. What is the significance of the coefficients in these equations?
5. Can we set up a similar problem with different quantities or prices? 

**Tip:** When solving systems of equations, the elimination method can be very effective for eliminating one variable at a time.

Flour is sold in 5kg and 2kg packets. The 5 kg packets cost $2.75 each, and the 2 kg packets cost $1.25 each. If the shop sells 67 kg of flour for a total of $38.50, how many of each size packet was sold?

Explore how to solve a system of equations involving the sale of flour packets of different weights and costs. This example includes key equations: 5x + 2y = 67 and 2.75x + 1.25y = 38.50. Suitable for students in Grades 7-10.

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