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Factory Work Flow

by Andrew
(New York)










































The workers in a factory produce widgets and whoosits. For each product, production time is constant and identical for all workers, but not necessarily equal for the two products. In one hour, 100 workers can produce 300 widgets and 200 whoosits. In two hours, 60 workers can produce 240 widgets and 300 whoosits. In three hours, 50 workers can produce 150 widgets and m whoosits. Find m.

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Jan 08, 2012
Factory Work Flow
by: Staff

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Part II


To begin solving for m, solve equations 1 and 2 to determine the values of x and y.

300x + 200y = 100
240x + 300y = 120

Multiply both sides of equation 2 by 2/3

(2/3) * (240x + 300y) = (2/3) * (120)

(2/3) * (240x) + (2/3) * (300y) = (2/3) * (120)

160x + 200y = 80


Subtract the modified version of equation 2 from equation 1

300x + 200y = 100
-(160x + 200y = 80)
-------------------------
300x - 160x + 200y -200y = 100 - 80

(300x - 160x) + (200y -200y) = 100 - 80

(140x) + (0) = 20

140x + 0 = 20

140x = 20


Divide each side of the equation by 140

140x/140) = 20/140

x*(140/140) = 20/140

x*(1) = 20/140

x = 20/140

x = 1/7 (it takes 1/7 of a man-hour to produce 1 widget)


substitute 1/7 for x in either equation 1 or equation 2, and then solve for y

240x + 300y = 120

240*(1/7) + 300y = 120


Multiply each side of the equation by 7

7*[240*(1/7) + 300y] = 7*120

7*[240*(1/7)] + 7*[300y] = 7*120

240 + 2100y = 840


Subtract 240 from each side of the equation

240 - 240 + 2100y = 840 - 240

0 + 2100y = 600

2100y = 600


Divide each side of the equation by 2100

2100y/2100 = 600/2100

y*(2100/2100) = 600/2100

y*(1) = 600/2100

y = 600/2100

y = 2/7 (it takes 2/7 of a man-hour to produce 1 whoosit)


Solve for m using equation 3. Substitute 1/7 for x and 2/7 for y.

150x + my = 150

150*(1/7) + m*(2/7) = 150


Multiply each side of the equation by 7

7*[150*(1/7) + m*(2/7)] = 7*150

7*[150*(1/7)] + 7*[m*(2/7)] = 7*150

150*(7/7) + *[m*2*(7/7)] = 7*150

150*(1) + [m*2*(1)] = 7*150

150 + 2m = 1050


Subtract 150 from each side of the equation

150 - 150 + 2m = 1050 - 150

0 + 2m = 900

2m = 900


Divide each side of the equation by 2

2m/2 = 900/2

m*(2/2) = 900/2

m*(1) = 450

m = 450



>>>>>>>>>>>>>>> The final answer is: m = 450 whoosits





Thanks for writing.
Staff

www.solving-math-problems.com


Jan 08, 2012
Factory Work Flow
by: Staff


Part I

Question:

by Andrew
(New York)


The workers in a factory produce widgets and whoosits. For each product, production time is constant and identical for all workers, but not necessarily equal for the two products. In one hour, 100 workers can produce 300 widgets and 200 whoosits. In two hours, 60 workers can produce 240 widgets and 300 whoosits. In three hours, 50 workers can produce 150 widgets and m whoosits. Find m.


Answer:

The workers in a factory produce widgets and whoosits.

For each product, production time is constant and identical for all workers, but not necessarily equal for the two products.

In one hour, 100 workers can produce 300 widgets and 200 whoosits.

The total number of man-hours used by 100 workers working for 1 hour = 100 man-hours

These 100 man-hours are divided between the production of widgets and whoosits.

(Man-hours used for widget Production) + (Man-hours used for whoosits Production) = 100

x = the number of hours it takes to produce 1 widget (hours per widget).

y = the number of hours it takes to produce 1 woosit (hours per woosit).


Therefore, the division of the hours between widgets and woosits can be expressed as the following equation:

300x + 200y = 100


In two hours, 60 workers can produce 240 widgets and 300 whoosits.

The total number of man-hours used by 60 workers working for 2 hours = 2*60 = 120 man-hours

The division of the hours between widgets and woosits can be expressed as the following equation:

240x + 300y = 120


In three hours, 50 workers can produce 150 widgets and m whoosits. Find m.

The total number of man-hours used by 50 workers working for 2 hours = 3*50 = 150 man-hours

The division of the hours between widgets and woosits can be expressed as the following equation:

150x + my = 150


The system of three equations which must be solved is:

Equation 1: 300x + 200y = 100
Equation 2: 240x + 300y = 120
Equation 3: 150x + my = 150

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