Car Wash Costs 14979E

1. **State the problem:** We have two car wash pricing plans: - Car Wash A charges a $10 membership fee plus $12 per wash. - Car Wash B charges no membership fee but $15 per wash. We want to write a system of equations to represent these costs and find the number of washes where the total cost is the same. 2. **Define variables:** Let $x$ = number of washes. Let $y$ = total cost. 3. **Write the equations:** - For Car Wash A: $$y = 10 + 12x$$ - For Car Wash B: $$y = 15x$$ 4. **Set the equations equal to find the number of washes where costs are equal:** $$10 + 12x = 15x$$ 5. **Solve for $x$:** $$10 = 15x - 12x$$ $$10 = 3x$$ $$x = \frac{10}{3}$$ 6. **Interpretation:** The costs are the same after $$\frac{10}{3}$$ washes, which is approximately 3.33 washes. Since washes must be whole numbers, the cost is the same between 3 and 4 washes. 7. **Graphing:** - The line for Car Wash A starts at $y=10$ and increases by 12 for each wash. - The line for Car Wash B starts at $y=0$ and increases by 15 for each wash. They intersect at $$x=\frac{10}{3}$$. **Final answer:** The number of washes where the cost is the same is $$x=\frac{10}{3}$$ (about 3.33 washes).