Subjects algebra

Taxicab Charges 683Ec4

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1. **State the problem:** We need to find the per-mile charge of Juan's taxicab company and compare it to Camila's per-mile charge, which is $2.30 per mile. 2. **Identify given information:** - Juan's company charges a pickup fee of $4 (from point (0,4)). - After 10 miles, the total charge is $18 (from point (10,18)). - Camila charges a pickup fee of $1.50 and $2.30 per mile. 3. **Find Juan's per-mile charge:** Use the slope formula for the line representing Juan's charges: $$\text{slope} = \frac{\text{change in cost}}{\text{change in miles}} = \frac{18 - 4}{10 - 0} = \frac{14}{10} = 1.4$$ 4. **Interpretation:** Juan charges $1.40 per mile plus a $4 pickup fee. 5. **Compare per-mile charges:** Camila charges $2.30 per mile, Juan charges $1.40 per mile. 6. **Calculate the difference:** $$2.30 - 1.40 = 0.90$$ 7. **Conclusion:** Camila charges $0.90 more per mile than Juan, not $0.20. **Final answer:** Camila's company charges $0.90 more per mile than Juan's.