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Detailed Solution for Word Problem of the Day

Discussion 

This may seem a little tricky at first.  But once it is read carefully it can be "dissected", and this is precisely the skill that is needed for higher levels of education and for more advance courses in mathematics.  Enjoy...

(click image below to enlarge)

How to dissect this problem

Dissecting this problem requires the student to read one section of the problem at a time and write down the math representation as they go along.  The goal of the problem is to find a math expression to represent the cost, c, of a taxi ride that is, d, miles.

"A taxi ride cost 50 cents for the first quarter of a mile..."

The student should stop right here, process this piece of information, make sure they understand this piece of information, then right down the math representation of this piece of information.

c=0.5

After this information has been properly processed and understood, then they should move on with processing more information from the problem.

"and"

(stop right here again because this is a "keyword")... students must be able to recognize the fact that "and" is a keyword that usually means to add something.  So in this case, we need a plus (+) sign.

c=0.5 +

So far so good.  Now the problem further states that 35 cents is charged for each additional quarter of a mile. So we know that we are charged 35 cents times "something".  So let's write that part down

c=0.5+0.35("something")

The "something" is "each additional quarter of a mile".  And the goal is to translate "each additional quarter of a mile" into the appropriate mathematical expression.

To figure out the math expression that goes in the parentheses, the logic goes like this:

1) I need to figure out how many "quarter miles" are in a mile. Answer: 4d

2) I need to subtract one (because the rate for the  first quarter mile is 0.5).

Therefore the expression that goes in the inside of the parenthesis is

4d-1

The full expression is

c=0.5 + 0.35(4d - 1)

The last sentence states that "the minimum charge for a taxi ride is 50 cents". This sentence should be translated mathematically to mean if d is less than 1/4 of a mile, then the charge is 50 cents.  Try plugging in a few values for d to see the values.

How did your students approach solving this problem? What are other observations you noticed?  Let us know below...

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