On a trip from the United States to Canada, Jenny took d U.S. dollars. She excha

Question

On a trip from the United States to Canada, Jenny took d U.S. dollars. She exchanged all of the money at the border receiving 10 Canadian dollars for every 7 U.S. dollars. After spending 90 Canadian dollars, she had d Canadian dollars left. Find a solution and explain your reasoning for each of the following using the most elementary math possible.

Write out clearn explanations for each step.

Connor was planning a trip to Canada and noticed the variability in the exchange rate. He planned to take d U.S. dollars and exchange it at the rate of c Canadian dollars to u U.S. dollars (c > u). After spending 90 dollars, he plans to have d Canadian dollars left. Write an expression for the amount of U.S. dollars he would have exchanged at the border.

Explanation / Answer

1.    the trip is from US to Canada

Jenny had d US dollars

for every 7 US dollars she is getting 10 Canadian dollars

means 1 UD dollar = 10/7 Canadian dollars

            for d US dollars = d X (10/7) canadian dollars she will get at the border

            now she has 10d/7 canadian dollars in total

now she spent 90 canadian dollars and left with d canadian dollars

   toatal canadian dollars = 90 canadian dollars + d canadian dollars

total she had 10d/7 canadian dollars

so 10d/7 = 90 + d

     10 d = 7 (90+d)

on solving this

   10d = 630 + 7d

   10d - 7d = 630

    3d = 630

    d= 630/3

   d = 210

so she has 210 US dollars

2. Connor is planing trip to canada

means he is going to canada from US

for u US dollars = c canadian dollars       example ( 5 chocolate = 15 dollar then

    1 US dollar = c/u canadian dollars            1 chocolare = 15 / 5 dollar )

now he has d US dollars means he will get (c/u)* d canadian dollars he will get.

     (c/u)* d canadian dollars, he spent 90 dollars and has d canadian dollars left with him

so   (c/u)* d canadian dollars = 90 canadian dollars + d canadian dollar

or   (c/u)* d = 90 + d

(c/u)* d - d = 90

d {(c/u) - 1 } = 90

d = 90/ {(c/u) - 1 }

d = 90u / (c-u)

so the amount of US dollars he would have exchannged at the border should be

d = 90u / (c-u)

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