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In a school picnic, a total of 43 students brought a backpack, a lunchbox, or both a backpack and a lunchbox. If there are a total of 23 backpacks and 25 lunchboxes, how many students brought both a backpack and a lunchbox? (A) 5 (B) 7 (C) 10 (D) 17 (E) 20 (ebasznan) m donoubraglion 2.32 25 LB

In a school picnic, a total of 43 students brought a backpack, a lunchbox, or both a backpack and a lunchbox. If there are a total of 23 backpacks and 25 lunchboxes, how many students brought both a backpack and a lunchbox? (A) 5 (B) 7 (C) 10 (D) 17 (E) 20 (ebasznan) m donoubraglion 2.32 25 LB

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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In a school picnic, a total of 43 students brought a backpack, a lunchbox, or both a backpack and a lunchbox. If there are a total of 23 backpacks and 25 lunchboxes, how many students brought both a backpack and a lunchbox? (A) 5 (B) 7 (C) 10 (D) 17 (E) 20 To solve this, we use the principle of inclusion-exclusion: Let: - \( A \) be the number of students with backpacks, - \( B \) be the number of students with lunchboxes, - \( X \) be the number of students with both items. According to the problem: - \( A + B - X = 43 \), - \( A = 23 \), - \( B = 25 \). Substituting \( A \) and \( B \): \[ 23 + 25 - X = 43 \] Simplifying: \[ 48 - X = 43 \] \[ X = 5 \] Thus, the number of students who brought both a backpack and a lunchbox is \( 5 \) (Option A).
Transcribed Image Text:In a school picnic, a total of 43 students brought a backpack, a lunchbox, or both a backpack and a lunchbox. If there are a total of 23 backpacks and 25 lunchboxes, how many students brought both a backpack and a lunchbox? (A) 5 (B) 7 (C) 10 (D) 17 (E) 20 To solve this, we use the principle of inclusion-exclusion: Let: - \( A \) be the number of students with backpacks, - \( B \) be the number of students with lunchboxes, - \( X \) be the number of students with both items. According to the problem: - \( A + B - X = 43 \), - \( A = 23 \), - \( B = 25 \). Substituting \( A \) and \( B \): \[ 23 + 25 - X = 43 \] Simplifying: \[ 48 - X = 43 \] \[ X = 5 \] Thus, the number of students who brought both a backpack and a lunchbox is \( 5 \) (Option A).
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