5. A train travels two different routes: the North Route and the South Route. • On Monday, the train traveled the North Route 8 times and the South Route 10 times, traveling a total of 410 miles. • On Tuesday, the train traveled the North Route 15 times and the South Route 11 times, traveling a total of 575 miles. How long is each route?

North Route is 20 miles, and South Route is 25 miles.

Step-by-step explanation:

Let the length of the North route be represented by x and that of the South route be represented by y.

On Monday,

8x + 10y = 410

On Tuesday,

15x + 11y = 575

So that,

8x + 10y = 410 .............. 1

15x + 11y = 575 ......... 2

Using substitution method, from equation 1;

x = ................. 3

Substitute the expression for x into equation 2,

15() + 11y = 575

multiply through by 8,

6150 - 150y + 88y = 4600

6150 - 62y = 4600

6150 - 4600 = 62y

1550 = 62y

divide through by 62 to have,

y = 25

Substitute the value of y in equation 3

x =

  =

  = 20

x = 20

Thus, North Route is 20 miles, and South Route is 25 miles.

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

step-by-step :