Abus travels two different routes the green route and the blue route the routes are different langths. 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.

The length of green route is 4.5 miles

Solution:

Let the length of green route be "x" miles

Let the length of blue route be "y" miles

On monday the bus traveled the green route 6 times and the blue route 5 times traveling a total of 52 miles

Therefore, we can frame a equation as:

6x + 5y = 52 ------- eqn 1

On Tuesday the bus traveled the green route 12 times and the blue route 13 times traveling a total of 119 miles

Therefore, we can frame a equation as:

12x + 13y = 119 -------- eqn 2

Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 2

12x + 10y = 104 -------- eqn 3

Subtract eqn 2 from eqn 3

12x + 10y = 104

12x + 13y = 119

( - ) --------------------

-3y = -15

3y = 15

y = 5

Substitute y = 5 in eqn 1

6x + 5(5) = 52

6x + 25 = 52

6x = 52 - 25

6x = 27

x = 4.5

Thus length of green route is 4.5 miles

answer:      

step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: