SOLUTION: From where he lives, it costs Jared $4 more for a round­trip train ticket to Chaska than it does for one to Waconia. Last month, Jared took round­trips to Chaska 7 times and to W

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Question 1189192: From where he lives, it costs Jared $4 more for a round­trip train ticket to Chaska than it does for one to Waconia. Last month, Jared took round­trips to Chaska 7 times and to Waconia 8 times. If he spent a total of $103 on train tickets, how much does Jared spend on one round­trip ticket to Waconia?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52817)   (Show Source): You can put this solution on YOUR website!
.
From where he lives, it costs Jared $4 more for a round­trip train ticket to Chaska
han it does for one to Waconia. Last month, Jared took round­trips to Chaska 7 times
and to Waconia 8 times. If he spent a total of $103 on train tickets, how much does
Jared spend on one round­trip ticket to Waconia?
~~~~~~~~~~~~~ 

Let x be the price of one round trip to Waconia, in dollars (the unknown value under the problem's question).

Then the price for one round trip to Chaska is (x+4) dollars.


Next, write the "money equation" as you read the problem

    7(x+4) + 8x = 103.


Now, simplify and find x

    7x + 28 + 8x = 103

    7x + 8x = 103 - 28

      15x   =  75

        x   = 75/15 = 5.


ANSWER.  The ticket for the round trip to Waconia and back costs 5 dollars.

Solved.



Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


You should know and understand how to set up and solve the problem using formal algebra, something like what the other tutor showed in her response.

But you can get some good mental exercise solving the problem mentally, with logical reasoning and simple arithmetic. It might go something like this:

The additional cost for a trip to Chaska is $4, so the extra cost for the 7 trips to Chaska is $28.
Subtract that from the total cost of $103 to find the remaining cost for the 7+8=15 trips is $75.
That means the cost of each of those trips is $75/15=$5.
So each trip to Waconia costs $5, and each trip to Chaska costs $5+$4 = $9.

ANSWER: A round trip ticket to Waconia costs $5.

Note that the calculations in this informal solution are EXACTLY the same as those used in the formal algebraic solution.
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