Question

Plz help meehhh :(((

A bus travels two different routes: the Green Route and the Blue Route. The routes are different lengths.

• On Monday the bus traveled the Green Route 6 times and the Blue Route 5 times, traveling a total of 52 miles.

• On Tuesday the bus traveled the Green Route 12 times and the Blue Route 13 times, traveling a total of 119 miles.


What is the length of the Green Route in miles?
A) 4.4 mi
B) 4.5 mi
C) 6.4 mi
D) 6.8 mi

Answer 1

B

Explanation:

Let length of Green Route be g and length of Blue Route be b

From 1st bullet point we can write the equation:

6g+5b = 52

From 2nd bullet, we can write:

12g + 13 b = 119

We can solve for b of the 1st equation as:

`6g+5b = 52\\5b=52-6g\\b=(52-6g)/(5)`

Now we can put this value of b into 2nd equation and solve for g (as shown below):

`12g+13b=119\\12g+13((52-6g)/(5))=119\\12g+(676-78g)/(5)=119\\(60g+676-78g)/(5)=119\\60g+676-78g=5*119\\60g+676-78g=595\\-18g=-81\\g=(-81)/(-18)=4.5`

Hence, the green route is 4.5 miles, B is right.