The weight of Jacob's 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?
$0.7(t)=t-4-2$
$0.7(t)=t+4+2$
$0.7 t(4+2)=t$
$0.7(t+4+2)=t$
Answer (1)
The problem states that 70% of the total weight of the backpack is textbooks. The total weight is the sum of the textbooks ( t ), notebooks (4 pounds), and the backpack (2 pounds). Therefore, the equation is 0.7 ( t + 4 + 2 ) = t .
Explanation
Problem Analysis Let's analyze the given information to form an equation that represents the weight of the textbooks.
Defining Total Weight Let t be the weight of the textbooks. The total weight of the backpack is the sum of the weight of the textbooks, the weight of the notebooks, and the weight of the backpack itself. So, the total weight is t + 4 + 2 .
Forming the Equation We are given that 70% of the total weight is the weight of the textbooks. Therefore, we can write the equation: 0.7 × ( t + 4 + 2 ) = t .
Identifying the Correct Option Comparing this equation with the given options, we find that the correct equation is 0.7 ( t + 4 + 2 ) = t .
Examples
Understanding how to set up equations based on weight distribution is useful in many real-life scenarios. For example, when planning a hiking trip, you might want to determine the optimal weight distribution in your backpack to ensure comfort and prevent strain. If you know the total weight you can carry and the percentage that should be allocated to water, food, and equipment, you can set up a similar equation to calculate the maximum weight for each category. This helps in packing efficiently and safely.
