1. **Problem statement:** Given the sequence of triangles with numbers 36, 48, and variable $a$ transforming to 24, variable $b$, and 80, find $a$ and $b$. 2. **Understanding the problem:** The transformation seems to scale the numbers proportionally. We can use ratios to find the unknowns. 3. **Step 1: Find the scale factor for the first number:** $$\text{Scale factor} = \frac{24}{36} = \frac{2}{3}$$ 4. **Step 2: Apply the scale factor to the second number to find $b$:** $$b = 48 \times \frac{2}{3} = 32$$ 5. **Step 3: Apply the scale factor to the third number to find $a$:** $$a = \frac{80}{\frac{2}{3}} = 80 \times \frac{3}{2} = 120$$ 6. **Summary:** - $a = 120$ - $b = 32$ Thus, the transformed sequence is 24, 32, 80.