Final answer:
To determine how many shapes can be made with 107 sticks, we need to find the pattern in the given examples. By observing the pattern, we can see that the number of sticks is increasing by 7 each time. Using this pattern, we can create an equation to solve for the number of shapes. By solving the equation, we find that 15 shapes can be made with 107 sticks.
Step-by-step explanation:
To determine how many shapes can be made with 107 sticks, we can start by finding the pattern in the given examples. We have 9 sticks, 16 sticks, and 23 sticks. By observing the pattern, we can see that the number of sticks is increasing by 7 each time. So, the next shape would have 30 sticks (23 + 7 = 30).
Now we can create an equation based on this pattern. Let 'n' represent the number of shapes and 's' represent the number of sticks. The equation would be: s = 9 + 7(n-1).
To find the number of shapes, we need to solve the equation for 'n' when 's' is equal to 107.
107 = 9 + 7(n-1)
107 - 9 = 7(n-1)
98 = 7(n-1)
14 = n-1
15 = n
Therefore, 15 shapes can be made with 107 sticks.