Answer:

The number of muffins sold by the students is:

• 25 muffins.

Step-by-step explanation:

First, we name the variables:

• C= Number of chocolate chip cookies sold.
• M= Number of muffins sold.

Now we establish the equations with the information given in the exercise:

1. C + M = 100
2. 0.5C + 1.25M = 68.75

We can use in this case the reduction method, to this, we multiply the first equation by (-0.5) obtaining the equation 3:

• [C + M = 100] * (-0.5) = -0.5C – 0.5M = -50

    3. -0.5C – 0.5M = -50

We operate the equations 2 and 3 to eliminate the variable C:

• (0.5C + 1.25M = 68.75) + (-0.5C – 0.5M = -50) = (0.75M = 18.75)

And we solve for the variable M:

• 0.75M = 18.75
• M = 18.75/0.75
• M = 25

We could stop here because we know the number of muffins now, but with the value for M, we can solve the value of C with the first equation to check the answer is correct:

• C + M = 100
• C + 25 = 100
• C = 100 – 25
• C = 75

In the end, we replace the values in the second equation and verify if the answer is correct:

• 0.5C + 1.25M = 68.75
• 0.5 * (75) + 1.25 * (25)  = 68.75
• 37.5 + 31.25 = 68.75
• 68.75 = 68.75