Sipho's taxi company charges R56,00 plus an additional R6,00 per kilometre for a trip. Madeleine's taxi company charges R8,00 per kilometre plus an additional R30,00 for a trip. A linear relationship exists between the cost in rand, $$ y $$, and the number of kilometres driven, $$ x $$. The cost is dependent on the number of kilometres driven. The distance, $$ x $$, at which the cost will be the same for both companies, is Select one: a. 134 km . b. 26 km . c. 56 km . d. 13 km .

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The distance where the cost is the same for both companies is 13 km. To find the distance $$ x $$ at which the cost will be the same for both taxi companies, we need to set up the cost equations for each company and then solve for $$ x $$. **Sipho's taxi company:** The cost $$ y $$ is given by: $$ y = 56 + 6x $$ where $$ 56 $$ is the base fare and $$ 6x $$ is the cost per kilometre. **Madeleine's taxi company:** The cost $$ y $$ is given by: $$ y = 8x + 30 $$ where $$ 8x $$ is the cost per kilometre and $$ 30 $$ is the base fare. To find the distance $$ x $$ where the costs are equal, we set the two equations equal to each other: $$ 56 + 6x = 8x + 30 $$ Now, we can solve for $$ x $$: 1. Rearranging the equation: $$ 56 - 30 = 8x - 6x $$ $$ 26 = 2x $$ 2. Dividing both sides by 2: $$ x = 13 $$ Thus, the distance at which the cost will be the same for both companies is $$ 13 $$ km. The correct answer is: **d. 13 km.**

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