Final answer:
To find the number of each size of ice cream cone sold, we can set up a system of equations based on the given information and solve using Cramer's rule. In this case, the number of single scoop cones is equal to the combined total of double and triple scoop cones. By solving the system of equations, we find that 30 single scoop cones, 40 double scoop cones, and 50 triple scoop cones were sold.
Step-by-step explanation:
To solve this problem, we can set up a system of equations based on the given information. Let x represent the number of single scoop cones, y represent the number of double scoop cones, and z represent the number of triple scoop cones.
From the given information, we know that x = y + z. We also know that the total number of cones sold is 120, so x + y + z = 120. Finally, the total cost of the cones sold is $134, so we can set up the equation 0.9x + 1.2y + 1.6z = 134.
To solve this system of equations using Cramer's rule, we can calculate the determinants of the coefficient matrix and the matrices obtained by replacing each column with the constants. Then, we can use these determinants to find the values of x, y, and z.
After solving the system of equations using Cramer's rule, we find that x = 30, y = 40, and z = 50. Therefore, 30 single scoop cones, 40 double scoop cones, and 50 triple scoop cones were sold.