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Below is the previous 3-day work schedule for co-workers: Kate, Kevin, and Greg, who work at a gold
mine. Unfortunately, someone must be fired.
Monday
Tuesday
Wednesday
Kate
8am-2pm
9am-2pm
10am-2pm
Kevin
9am-4pm
8am-1pm
8am-4pm
Greg
8am-12pm
12pm-6pm
9am-3pm
If there were 51 gold nuggets found on Monday, 55 nuggets found on Tuesday, and 54 nuggets found on
Wednesday,
1.) How many nuggets per hour does each worker find? (These three numbers is the next code)
2.) Who should be fired?

Below is the previous 3day work schedule for coworkers Kate Kevin and Greg who work at a gold mine Unfortunately someone must be fired Monday Tuesday Wednesday class=

Respuesta :

The three workers working in different shifts, and the number of gold

nuggets found in three days give a system of three equations.

Response:

1) Kate finds 4 nuggets per hour, Kevin finds 1 nugget per hour and Greg finds 5 nuggets per hour.

2) Kevin

Which method can be used to solve for the number of nuggets each worker finds per hour?

Let a, b, and c represent the number of nuggets per hour that Kate, Kevin, and Greg finds, we have;

Kate, Kevin, and Greg works for 6, 7, and 4 hours respectively on Monday

On Tuesday, we have; 5, 5, and 6 hours respectively

On Wednesday, we have; 4, 8, and 6 hours respectively

Which gives the following system of simultaneous equations;

6·a + 7·b + 4·c = 51...(1)

5·a + 5·b + 6·c = 55...(2)

4·a + 8·b + 6·c = 54...(3)

Subtracting equation (2) from (3) gives;

4·a - 5·a + 8·b - 5·b + 6·c - 6·c = 54 - 55 = -1

3·b - a = -1

a = 3·b + 1

Which gives;

6·(3·b + 1) + 7·b + 4·c = 25·b + 4·c + 6 = 51

25·b + 4·c + 6 = 51

  • [tex]c = \dfrac{51 - 6 - 25\cdot b}{4} = \mathbf{ \dfrac{45 - 25\cdot b}{4}}[/tex]

5·(3·b + 1) + 5·b + 6·c = 20·b + 6·c + 5  = 55

20·b + 6·c + 5 = 55

Similarly;

  • [tex]c = \dfrac{55-5 - 20\cdot b}{6} = \mathbf{\dfrac{50 -20\cdot b}{6}}[/tex]

Which gives;

  • [tex]c = \dfrac{45-25\cdot b}{4} = \dfrac{50- 20\cdot b}{6}[/tex]

4 × (50 - 20·b) = 6 × (45 - 25·b)

200 - 80·b = 270 - 150·b

150·b - 80·b = 270 - 200 = 70

70·b = 70

  • b = 1

a = 3·b + 1

a = 3 × 1 + 1 = 4

  • a = 4

[tex]c = \dfrac{45-25\times 1}{4} = \mathbf{ 5}[/tex]

  • c = 5

  • Number of gold nuggets Kate finds per hour, a = 4
  • Number of gold nuggets Kevin finds per hour, b = 1
  • Number of gold nuggets Greg finds per hour, c = 5

2.) The person that can be fired is the one that finds the least number of gold nuggets per hour, which is Kevin

Learn more about simultaneous equations here:

https://brainly.com/question/867837

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