manufactures small electronic components called diodes. Each diode is worth $1.50. Plant A produced 4443 diodes and Plant B produced 5557 diodes. The supervisor was asked what the total value of all the diodes was. The supervisor immediately responded "$15,000." The supervisor would not have been able to compute the value so quickly if he had to multiply $1.50 by 4443 and then add this to the result of $1.50 times 5557. Explain how you think the supervisor got the answer so quickly? $1.50
manufactures small electronic components called diodes. Each diode is worth $1.50. Plant A produced 4443 diodes and Plant B produced 5557 diodes. The supervisor was asked what the total value of all the diodes was. The supervisor immediately responded "$15,000." The supervisor would not have been able to compute the value so quickly if he had to multiply $1.50 by 4443 and then add this to the result of $1.50 times 5557. Explain how you think the supervisor got the answer so quickly? $1.50
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question
Transcribed Image Text:### Manufacturing Problem
**Context:**
A company manufactures small electronic components called diodes. Each diode is worth $1.50. There are two production plants:
- **Plant A** produced 4,443 diodes.
- **Plant B** produced 5,557 diodes.
**Problem Statement:**
The supervisor was asked to calculate the total value of all the diodes. Without performing detailed calculations, the supervisor quickly responded with a total value of **$15,000**. The question is how the supervisor arrived at this total so promptly when one would typically multiply the number of diodes produced by each plant by $1.50 and then sum the results.
**Objective:**
Explain the reasoning behind the supervisor's rapid computation of the total value. What shortcut or logical reasoning might the supervisor have used to arrive at the solution quickly?
**Considerations:**
Calculate the actual total value using the following steps and consider any estimation techniques:
1. Calculate the total number of diodes from both plants:
- Total diodes = 4,443 (Plant A) + 5,557 (Plant B).
2. Calculate the total value using the unit price:
- Total value = Total diodes × $1.50.
3. Compare with the supervisor’s estimated total of $15,000 and explore possible estimation methods or shortcuts.
Expert Solution
Step 1
Given that : value of each diode = $ 1.50
plant A reduces number of diodes = 4443
Plant B reduces number of diodes = 5557
To find : How the supervisor find the total value of diodes as $ 15000.
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