On a trip from the United States to Canada, Jenny took d U.S. dollars. She excha
ID: 3010452 • Letter: O
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)