Solve the problem using both methods and compare the answers.
Answer: Yes Explanation: See solution.
Practice makes perfect
The solution of a problem is the value that makes it true. Thus, the solution method does not change the solution. We will solve the problem using Alexa's method and Zack's method, then compare the answers.
Alexa's method
Let's organize the given information using a table. Alexa assumes there are initially m miles on Car B.
Car
Initial Miles
Miles After One Hour
A
m+50
m+50 + 50
m+100
B
m
m + 50
m+50
C
m-30
m-30 + 50
m+20
The problem says that after one hour, twice the number of miles on Car A is 70 miles less than 3 times the number of miles on Car C.
2 (m+100) = 3 (m+20) -70
Let's solve the above equation to find the value of m.
We found that m=210 and thus, following Alexa's method, there were initially 210miles on Car B.
Zack's method
Let's use a table again to organize the given information. Zack assumes there are initially m miles on Car C.
Car
Initial Miles
Miles After One Hour
A
m+80
m+80 + 50
m+130
B
m+30
m+30 + 50
m+80
C
m
m + 50
m+50
Recalling again what the problem says, after one hour twice the number of miles on Car A is 70 miles less than 3 times the number of miles on Car C.
2 (m+130) = 3 (m+50) -70
Let's solve the above equation to find the value of m.
We found that m=180 and thus there were initially 180miles on Car C. Let's use this to find how many miles Car B initially had.
Car B:& m+30⇒ 180+30=210miles
Following Zack's method, we found that there were initially 210miles in Car B. Both methods lead to the same answer.
