For journeys between nine am and four pm, a cab company charges a fixed fare of three dollars plus 30 cents per fifth of a mile. A cab fare is seven dollars 50. Write an equation that could be used to find 𝑑, the distance travelled.
It costs 30 cents to travel one-fifth of a mile. We need to work out how much it would cost to travel one mile. Multiplying both side by five shows that it costs 150 cents to travel one mile. 150 cents is the same as one dollar 50. Therefore, it costs one dollar 50 to travel one mile.
As 𝑑 is the number of miles travelled, we can say that the cost would be 1.5 multiplied by 𝑑, or 1.5𝑑. We then need to add the fixed fare of three dollars. This gives us 1.5𝑑 plus three. As the cab fare was seven dollars 50, we can put this equation equal to 7.5. 1.5𝑑 plus three is equal to 7.5.
In this particular question, we were only asked to write the equation: 1.5𝑑 plus three equals 7.5. However, we could use this to work out the distance travelled. Subtracting three from both sides of the equation gives us 1.5𝑑 equals 4.5, as 7.5 minus three is 4.5. Dividing both sides of this equation by 1.5 gives us a value of 𝑑 equal to three. This means that the distance travelled was three miles. We could check this answer by substituting 𝑑 equals three back into the equation.