A taxicab charges $4.25 for the first mile and $1,50 for each additional mile. Write a rule for describing the total rater as a function of the total miles m. What is the taxi rate for 12 miles?

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Answer 1 · 2016-10-27T16:31:05

$Total charge = $ 4.25 + $ 1.50 (m - 1)$ $"Total charge "=$4.25+$1.50(m-1)$

$Total charge for 12 miles = $ 20.75$ $"Total charge for 12 miles " =" "$20.75$

$Building the rule$ $color(blue)("Building the rule")$

The trick with algebra is to think what you would do with numbers, then substitute letters.

Mile number 1 costs $$ 4.25$ $$4.25$

The rest of the miles $\Rightarrow (total miles - 1) \times $ 1.50$ $=>("total miles "-1)xx$1.50$

Putting this all together we have:

$$ 4.25 + (total miles - 1) \times $ 1.50$ $$4.25 +("total miles "-1)xx$1.50$

The question instructs that we are to use the letter m for the total miles so we now have:

$$ 4.25 + (m - 1) \times $ 1.50$ $$4.25 +(m-1)xx$1.50$

This would be written as:

$$ 4.25 + $ 1.50 (m - 1)$ $$4.25 +$1.50(m-1)$

So $Total charge = $ 4.25 + $ 1.50 (m - 1)$ $" Total charge "=$4.25+$1.50(m-1)$

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$Determine the charge for 12 miles$ $color(blue)("Determine the charge for 12 miles")$

$Total charge = $ 4.25 + $ 1.50 (12 - 1)$ $" Total charge "=$4.25+$1.50(12-1)$

$Total charge = $ 4.25 + $ 1.50 (11)$ $" Total charge "=$4.25+$1.50(11)$

$Total charge for 12 miles = $ 4.25 + $ 16.50 = $ 20.75$ $" Total charge for 12 miles "=$4.25+$16.50" " =" "$20.75$