Math problem please help

A student bake sale is selling baked goods. In total they sell 100 pieces of baking, Chocolate chip cookies sell for $0.50 and Muffins for $1.25. The total money earned from the bake sale came to 68.75. How many muffins did they sell?

Answer:The number of muffins sold by the students is:

.25 muffinsStep-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:

C + M = 1000.5C + 1.25M = 68.75We 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 = -503.

-0.5C – 0.5M = -50We 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 = 18.75M = 18.75/0.75M = 25We 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 = 100C + 25 = 100C = 100 – 25C = 75In the end, we replace the values in the second equation and verify if the answer is correct:

0.5C + 1.25M = 68.750.5 * (75) + 1.25 * (25) = 68.7537.5 + 31.25 = 68.7568.75 = 68.75