1. **Problem Statement:** We need to find the total cost for each company (Thunder Cable and Flash Cable) for the first 12 gigabytes of data usage. 2. **Formula:** Total cost for each company is given by: $$\text{Total Cost} = \text{Activation Fee} + (\text{Cost per GB} \times \text{Number of GB})$$ 3. **Given Data:** - Thunder Cable: Activation Fee = 46, Cost per GB = 5.50 - Flash Cable: Activation Fee = 61, Cost per GB = 4.00 4. **Calculate costs for each gigabyte from 1 to 12:** For Thunder Cable: $$\text{Cost} = 46 + 5.50 \times x$$ For Flash Cable: $$\text{Cost} = 61 + 4.00 \times x$$ where $x$ is the number of gigabytes. 5. **Example calculations:** - For 1 GB: - Thunder Cable: $46 + 5.50 \times 1 = 46 + 5.50 = 51.50$ - Flash Cable: $61 + 4.00 \times 1 = 61 + 4 = 65$ - For 12 GB: - Thunder Cable: $46 + 5.50 \times 12 = 46 + 66 = 112$ - Flash Cable: $61 + 4.00 \times 12 = 61 + 48 = 109$ 6. **Summary Table:** | GB | Thunder Cable Cost | Flash Cable Cost | |----|--------------------|------------------| | 1 | 51.50 | 65 | | 2 | 57.00 | 69 | | 3 | 62.50 | 73 | | 4 | 68.00 | 77 | | 5 | 73.50 | 81 | | 6 | 79.00 | 85 | | 7 | 84.50 | 89 | | 8 | 90.00 | 93 | | 9 | 95.50 | 97 | | 10 | 101.00 | 101 | | 11 | 106.50 | 105 | | 12 | 112.00 | 109 | 7. **Interpretation:** Thunder Cable starts cheaper but becomes more expensive than Flash Cable after about 10 GB.