Question

Two cab rides cost the same amount for the same number of miles, m. Which situation can be represented by the equation 2.50 + 0.50m = 1.00 + 0.75m?

Answer 1

One cab charges an initial fee of $2.50 and then $0.50 for every mile. The other cab company charges an initial fee of $1.00 and then $0.75 for every mile.

Explanation:

Answer 2

If the number of miles is 6

Explanation:

Since they vary with different rates ($/mile in our case), such equality can only be true for a specific amount of miles. Less miles and the left part ($2.50...) would be higher, more miles and the right part ($1.00...) would be higher because it grows faster.

So, that's the number of miles for which the equation is true?

2.50 + 0.50m = 1.00 + 0.75m

Let's regroup similar terms:

1.50 = 0.25m

the isolate m

m = 6

So, if the ride covers 6 miles, the equation is true:

2.5 + 0.5 (6) = 1.00 + 0.75 (6)

2.5 + 3 = 1 + 4.50

5.5 = 5.5