91Ó°ÊÓ

The infamous band Slippery Even When Dry ended their concert and checked into the Fuzzy Fig Motel. The guys in the band (Spike, Slip, and Milly) decided to share a room. They were told by Chip, the night clerk who was taking a home- study course on animal husbandry, that the room cost \(\$ 25\) for the night. Milly, who took care of the finances, collected \(\$ 10\) from each band member and gave Chip \(\$ 30\). Chip handed Milly the change, \(\$ 5\) in singles. Milly, knowing how bad Slip and Spike were at arithmetic, pocketed two of the dollars, turned to the others, and said, "Well guys, we got \(\$ 3\) change, so we each get a buck back." He then gave each of the other two members a dollar and pocketed the last one for himself. Once the band members left the office, Chip, who witnessed this little piece of deception, suddenly realized that something strange had just happened. Each of the three band members first put in \(\$ 10\) so there was a total of \(\$ 30\) at the start. Then Milly gave each guy and himself \(\$ 1\) back. That means that each person put in only \(\$ 9\), which is a total of \(\$ 27\) ( \(\$ 9\) from each of the three). But Milly had skimmed off \(\$ 2\), so that gives a total of \(\$ 29\). But there was \(\$ 30\) to start with. Chip wondered what happened to that extra dollar and who had it. Can you please resolve and explain the issue to Chip?

Step by step solution

01

Initial Collection

The initial amount collected from the band members is \(10 + 10 + 10 = 30\) dollars.

02

Payment for the Room

The room cost \(25\) dollars, so Milly paid \(30\) dollars and received \(5\) dollars as change from Chip.

03

Distributing the Change

Milly kept \(2\) dollars for himself and gave \(1\) dollar back to each of Slip and Spike, distributing \(3\) dollars total back to the band members.

04

Clarifying the Confusion

Initially, each band member contributed \(10\) dollars, but after receiving \(1\) dollar back, each effectively spent \(9\) dollars. The confusion arises when trying to sum the \(27\) dollars spent by the band members and the \(2\) dollars retained by Milly. These \(29\) dollars already account for the 2 dollars Milly kept.

05

Correct Calculation

Each of the band members ended up spending \(9\) dollars, which totals \(27\) dollars for the room. Out of these collected \(27\) dollars, \(25\) dollars was paid for the room, and \(2\) dollars were pocketed by Milly. Thus, the calculations correctly account for all \(30\) dollars initially given.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Problem Solving

In problem solving, understanding the scenario and effectively breaking it down into steps is key. This exercise is a great example of utilizing problem solving in real-world settings. The challenge here involves recognizing where the initial misunderstanding arises.

First, it's important to untangle each transaction step-by-step to see where every dollar goes. Each band member contributes $10, which totals $30. From this, we subtract the room cost of $25, leaving $5 in change. By distinguishing these initial steps, the problem is framed correctly, allowing for a methodical approach to reach a solution.

Problem solving is about clarifying confusion, understanding each transaction, and establishing a clear sequence of events. This scene ensures no dollar is lost or unaccounted for, preventing unnecessary puzzles and frustrations.

Arithmetic

Arithmetic involves the basic operations of addition, subtraction, and multiplication, which are crucial in solving this exercise. Each calculation should be clear and precise to avoid mistakes.

• The initial collection is $10 from each member: $10 + $10 + $10 = $30.
• The room costs $25, leaving $30 - $25 = $5 in change.
• Milly distributes $3 as $1 to each member and keeps $2 himself, demonstrating subtraction within money distribution.

Arithmetic is about precision and ensuring that each dollar is accounted for. The key attribute of arithmetic is its logical structure, which helps clarify how money moves through the transaction chain and prevents false assumptions.

Logical Reasoning

Logical reasoning combines both arithmetic and problem-solving skills to provide clarity in confusing situations. In this exercise, logical reasoning helps explain why the calculations always add up to $30 despite appearing otherwise.

Each band member effectively spends $9 after receiving $1 back. Together the total is $27. This is where logical reasoning comes in. Instead of trying to match a total alongside the skimming, realize that the initial $27 includes both the room cost and Milly's hidden $2. Thus, validating the integrity of the transactions.

Logical reasoning is crucial to identify misunderstandings and assure all involved parties understand the importance of tracking each step within financial transactions.