The fair will be traveling to a place that uses the metric system. They received directions to their next stop, but they are in kilometers. They will need to convert their distances in miles to kilometers. Arlene takes the number of miles, doubles it, and then subtracts 20% of the result. Raul divides the number of miles by 5, then multiplies the result by 8. Write an algebraic expression for each method. Are these expressions equivalent?

2x - 0.4x ;

8x/5 ;

Yes

Step-by-step explanation:

Let number of miles = x

Arlene:

Double number of miles = 2 * x = 2x

Subtract 20% of the result :

2x - 20% of 2x ;

2x - 0.4x

Raul:

Divides Number of miles by 5 ; x / 5

Multiplies result by 8 ;

8 * (x/5) = 8x /5

To know if expressions are equivalent :

Let x = 10 miles

Using Arlene's expression:

2x - 0.4x

x = 10

2(10) - 0.4(10) = 16

Using Raul's expression :

8x / 5

(8*10) / 5

80/5

= 16

Since they give the same result, we can conclude that the expression are equivalent