←
Recognizing Related Equations

1.6.4 Recognizing Related Equations

1.6.4 • Recognizing Related Equations

Cool Down

A cardboard box, which weighs 0.6 pound when empty, is filled with 15 bags of beans and a 4-pound bag of rice. The total weight of the box and the contents inside it is 25.6 pounds. One way to represent this situation is with the equation 0.6+15b+4=25.60.6+15b+4=25.6.

1.

In this situation, what does the solution to the equation represent?

The solution is the weight of a bag of beans.

2.

Identify the three equations that are equivalent to 0.6+15b+4=25.6.

  1. 15 b + 4 = 25.6 15b+4=25.6
  2. 15 b + 4 = 25 15b+4=25
  3. 3 ( 0.6 + 15 b + 4 ) = 76.8 3(0.6+15b+4)=76.8
  4. 15 b = 25.6 15b=25.6
  5. 15 b = 21 15b=21

15b+4=2515b+4=25, 3(0.6+15b+4)=76.83(0.6+15b+4)=76.8, 15b=2115b=21. Correctly applying the properties of real numbers and using inverse operations helps you recognize equivalent equations.