Question

the weight of jacobs backpack is made up of the weight of the contents of the backpack as well as the weight of the backpack itself. seventy percent of the total weight is textbooks. his notebooks weigh a total of 4 pounds, and the backpack itself weighs 2 pounds. if the backpack contains only textbooks and notebooks, which equation can be used to determine \\(t\\), the weight of the textbooks?

\\(0.7(t) = t - 4 - 2\\)
\\(0.7(t) = t + 4 + 2\\)
\\(0.7t(4 + 2) = t\\)
\\(0.7(t + 4 + 2) = t\\)

Explanation:

Define the total weight of the backpack

Using the Linear Equation Solving knowledge point
Let \(W\) represent the total weight of the backpack.
The total weight is the sum of the weights of its components:

• Textbooks: \(t\)
• Notebooks: \(4\) pounds
• Backpack itself: \(2\) pounds

Thus, the total weight is:

$$W = t + 4 + 2$$

Set up the percentage relationship

The problem states that seventy percent of the total weight is textbooks.
We can write this relationship as:

$$0.7 \cdot W = t$$

Substitute the total weight expression

Substitute the expression for \(W\) from the first step into the percentage equation:

$$0.7(t + 4 + 2) = t$$

Answer:

• 0.7(t) = t - 4 - 2
• 0.7(t) = t + 4 + 2
• 0.7t(4 + 2) = t
• 0.7(t + 4 + 2) = t (Correct answer)