Question

1. mary puts 54 of her stamps in a book. the book holds 96 stamps. how many more stamps can mary put in the book? part a complete the bar diagram to model the problem. 96 54 explain how the bar diagram helps you understand the problem. part b write an equation to solve the problem.

Explanation:

Part A

Step1: Analyze the bar diagram

The top bar represents the total capacity of the book, which is 96 stamps. The bottom bar is split into two parts: one part is the number of stamps already put in (54), and the other part is the number of additional stamps that can be put in (let's call this \( x \)). So the bottom bar should sum to 96, meaning \( 54 + x = 96 \). Visually, the top bar is a single segment of 96, and the bottom bar has a segment of 54 and a missing segment (the one we need to find) that together equal 96.

Step2: Explain the bar diagram's help

The bar diagram helps by visually representing the total (96) as a whole and showing that it's composed of the stamps already placed (54) and the stamps that can still be placed. This makes it clear that we need to find the difference between the total and the already used amount, which is a subtraction problem (or an addition problem to check).

Part B

Step1: Define the variable

Let \( x \) be the number of more stamps Mary can put in the book.

Step2: Set up the equation

The total capacity of the book (96) is equal to the number of stamps already in the book (54) plus the number of additional stamps (\( x \)). So the equation is \( 54 + x = 96 \). To solve for \( x \), we can also write it as \( x = 96 - 54 \) (by subtracting 54 from both sides of the equation \( 54 + x = 96 \)).

Step3: Solve the equation

Calculating \( 96 - 54 \), we get \( x = 42 \).

Answer:

(Part A Explanation):
The top bar is labeled 96 (total capacity). The bottom bar has one segment labeled 54 (stamps already in) and the other segment (to be filled) represents the additional stamps. The bar diagram shows the total as the sum of the two parts of the bottom bar, so we know to find the missing part by relating 54, the missing part, and 96.