Question

each situation can be modeled with an equation and with a tape diagram.

• aria wants to place 20 books on 4 shelves. each shelf holds the same number of books. there are 4 books that do not fit.
• omar makes a tower with 4 red blocks and b blue blocks. then he makes three more towers that are the same. he uses 20 blocks total.

drag each model into a column to represent the situation. answer choices may be used only once.
aria’s books omar’s blocks

Explanation:

Analyzing Ana's Books Situation

Step1: Define variables

Let \( x \) be the number of books per shelf. There are 4 shelves, so books on shelves: \( 4x \). 4 books don't fit, total books: 20.

Step2: Form equation

\( 4x + 4 = 20 \)

Step3: Solve for \( x \)

Subtract 4: \( 4x = 20 - 4 = 16 \)
Divide by 4: \( x = \frac{16}{4} = 4 \)

Analyzing Omar's Blocks Situation

Step1: Define variables

1 tower: \( 4 + b \) blocks. 4 towers: \( 4(4 + b) \) blocks. Total blocks: 20.

Step2: Form equation

\( 4(4 + b) = 20 \)

Step3: Solve for \( b \)

Divide by 4: \( 4 + b = \frac{20}{4} = 5 \)
Subtract 4: \( b = 5 - 4 = 1 \)

Answer:

(for Ana's books per shelf): \( 4 \)