Question

ann is making her grandfather a scrapbook for his birthday. the scrapbooking kit she bought has 15 fewer pieces of colored paper than pieces of white paper. the scrapbooking kit has w pieces of white paper and 35 pieces of colored paper.
which diagram models the story?
two green bar diagrams: first with w, second with 35 and a segment 15 to the right; then another two green bar diagrams: first with 35, second with w and a segment 15 to the right
which equation models the story?
$w + 15 = 35$ $w - 15 = 35$

Explanation:

Part 1: Which diagram models the story?

The problem states that colored paper (35 pieces) is 15 fewer than white paper (\(w\) pieces). So white paper should be longer (more) than colored paper. The first diagram has \(w\) as the longer bar and 35 with a 15 - length gap (showing 35 + 15 = \(w\)), which matches the relationship (colored is 15 less than white). The second diagram incorrectly has 35 as the longer bar. So the first diagram (with \(w\) as the top bar, 35 and 15 as the bottom) models the story.

Step1: Analyze the relationship

Colored paper (35) is 15 fewer than white paper (\(w\)). So white paper minus 15 equals colored paper.

Step2: Form the equation

Mathematically, this is \(w - 15=35\) (since \(w\) (white) minus 15 (the difference) gives 35 (colored)). The other equation \(w + 15 = 35\) would imply white is less than colored, which is wrong.

Answer:

The first diagram (top - \(w\), bottom - 35 and 15)

Part 2: Which equation models the story?