Question

3a. Show that the following equations is equivalent to 0.9C + 1.89r = 17.01Then, explain when it might be helpful to write the equation in these forms.c=18.9 -2.1r3b. Show that the following equations is equivalent to 0.90 +1.89r = 17.01Then, explain when it might be helpful to write the equation in these forms.r=c+9

Answer 1

We can easily get c=18.9 -2.1r from 0.9C + 1.89r = 17.01 by following these steps:

1. subtract 1.89r on both sides

0.9C + 1.89r = 17.01

0.9C + 1.89r - 1.89r = 17.01 - 1.89r

0.9c = 17.01 - 1.89r

2. Divide both sides for 0.9

0.9c/0.9 = 17.01/0.9 - 1.89r/0.9

c = 18.9 - 2.1r

It is usefull to have the form c = 18.9 - 2.1r of this equation when we have a value of r and we want to find the corresponding c-pair.

Similarly for the equation 0.9c +1.89r = 17.01, we can get r=c+9 like this:

1.

0.9c +1.89r = 17.01

1.89r = 17.01 - 0.9c

2.

1.89r/1.89 = 17.01/1.89 - 0.9c/1.89

r = 9 - r10/21