Question

What If? 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 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?
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.

Answer 1

1. 310 miles

2. Yes, the final value of miles for car A,B&C in both formulas is the same

Explanation:

Using Zack method, lets assume there are m miles on car C

Car C=m miles

Car B= 30 miles more than those in car C = m+30 miles

Car A= 50 miles more that those in car B= 50+m+30= m+80 miles

Given after 1 hour of travel covers 50 miles

Car C=m-50 miles

Car B=m+30-50=m-20 miles

Car A= m+80-50 = m+30 miles

Condition

After 1 hour twice the miles covered by car A is less 70 miles , three times the miles on car C

This means

2(30+m) + 70 = 3(m-50)-------------------solve for m

60+2m+70=3m-150

130+2m=3m-150

130+150=3m-2m

280=m

Answers

Initial number of miles in ;

Car A=m+80 = 280+80= 360 miles

Car B= m+30 = 280+30=310 miles

Car C= m= 280 miles

Using Alexa formula

Initial

Car A=m+50 miles

Car B= m miles

Car C= m-30 miles

After 1 hour, subtract 50 miles from each car

Car A= m+50-50 = m miles

Car B= m-50 miles

Car C= m-30-50= m-80 miles

Condition

Twice the number of miles on Car A is 70 miles less than three times the number of miles on car C

2m+70=3(m-80)

2m+70=3m-240

70+240=3m-2m

310=m

Answers

Initial;

Car A=m+50=310+50=360 miles

Car B=m= 310 miles

Car C= m-30 =310-30=280 miles

Conclusion

Zack's answer will be the same as Alexa's answers.Changing the position of the variable m doesnot affect final results of miles in the cars.