Question 987464: Alexa and Zack are solving the following problem: The number of miles on Car A is 50 miles more than the number of miles on Car B, and the number of miles on Car B is 30 miles more than the number of miles on Car C. All the cars travel 50 miles in 1 hour. After 1 hour, twice the number of miles Car A is 70 miles less than 3 times the number of miles on Car C. How many miles were there on Car B initially? Alexa assumes there are m miles on Car B. Zack assumes there are m miles on Car C. Will Zack's answer be the same as Alexa's answer? Explain.
Found 3 solutions by ankor@dixie-net.com, Silver_surfer, greenestamps:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Alexa and Zack are solving the following problem:
The number of miles on Car A is 50 miles more than the number of miles on Car B,
a = b+50
and the number of miles on Car B is 30 miles more than the number of miles on Car C.
b = c+30
or
c = b-30
All the cars travel 50 miles in 1 hour.
All travel at 50 mph
After 1 hour, twice the number of miles Car A is 70 miles less than 3 times the number of miles on Car C.
2(a+50) = 3(c+50) - 70
2a + 100 = 3c + 150 - 70
2a = 3c + 150 - 70 - 100
2a = 3c - 20
Replace a with (b+50), replace c with (b-30)
2(b+50) = 3(b-30) - 20
2b + 100 = 3b - 90 - 20
2b + 100 = 3b - 110
2b = 3b - 110 - 100
2b = 3b - 210
210 = 3b - 2b
b = 210 mi car B initially
then
a = 210 + 50
a = 260 car A initially
and
c = 210 - 30
c = 180 mi Car C initially
Alexa assumes there are m miles on Car B.\
Zack assumes there are m miles on Car C.
Will Zack's answer be the same as Alexa's No
Answer by Silver_surfer(1)  (Show Source):
You can put this solution on YOUR website! Alexa and Zack are solving the following problem: The number of miles on Car A is 50 miles more than the number of miles on Car B, and the number of miles on Car B is 30 miles more Car C. All the cars travel 50 miles in 1 hour. After 1 hour, twice the number of miles on Car A is 70 miles less than 3 times the number of miles on Car C.
How many miles were there on Car B initially?
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set Car A = a
set Car B = b
set Car C = c
a = 50 + b
b = 30 + c
2a = 3c - 70 rewritten c = (2a+70)/3
b = 30 + c
b = 30 + (2a+70)/3 substitute c
b = 30 + [2(50 + b) + 70 )]/3 substitute a
3b = 90 + 100 + 2b + 70 multiply both sides by 3
b = 260 simplify
Car B had 260 miles initially.
Car A had 310 miles
Car C had 230 miles
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Alex assumes Car B has m miles.
Zack assumes Car C has m miles.
Will Zack’s answer be the same as Alex’s? No.
There can be one correct answer and since Car B and Car C had different miles, Zack is incorrect.
Answer by greenestamps(13195)  (Show Source):
You can put this solution on YOUR website!
Ignore the solution from the other tutor. It does not use all of the given information to set up the problem correctly; and it does not interpret the question that is asked correctly.
The two students are solving the same problem in different ways; as long as their work is correct, they should (and will) get the same answer.
The given information is that car A has 50 more miles than car B and car B has 30 more miles than car C.
Alexa's solution....
Let m = miles on car B
Then m+50 = miles on car A
and m-30 = miles on car C
After 1 hour at 50mph, the numbers of miles on each car are
A: m+100
B: m+50
C: m+20
At that time, twice the number of miles on car A is 70 less than 3 times the number of miles on car C:
2(m+100)=3(m+20)-70
2m+200=3m-10
m=210
Alexa's answer: the number of miles on car B initially was m=210.
Zack's solution....
Let m = miles on car C
Then m+30 = miles on car B
and m+80 = miles on car A
After 1 hour at 50mph, the numbers of miles on each car are
A: m+130
B: m+80
C: m+50
At that time, twice the number of miles on car A is 70 less than 3 times the number of miles on car C:
2(m+130)=3(m+50)-70
2m+260=3m+80
m=180
Zack's answer: the number of miles on car B initially was m+30=210.
ANSWER: Zack's answer will be the same as Alexa's.
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