Part 1. 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 = 25.6.

Select all equations that are also equivalent to 0.6 + 15b + 4 = 25.6.

Responses

Equation A: 15b + 4 = 25.6
Equation A: 15b + 4 = 25.6

Equation B: 15b + 4 = 25
Equation B: 15b + 4 = 25

Equation C: 3(0.6 + 15b + 4) = 76.8
Equation C: 3(0.6 + 15b + 4) = 76.8

Equation D: 15b = 25.6
Equation D: 15b = 25.6

Equation E: 15b = 21


Part 2. To solve the equation 7.5d = 2.5d, Lin divides each side by 2.5d, and Elena subtracts 2.5d from each side.

a. Will both moves lead to the solution? Explain your reasoning.

b. What is the solution?


Part 3. The equation 4(x – 2) = 100 is a true equation for a particular value of x. Explain why 2(x – 2) = 50 is also true for the same value of x.