East Texas Seasonings is preparing to build one processing centre to serve its four sources of seasonings. The four source locations are at coordinates shown below. Also, the volume from each source is provided. What is the centre of gravity? $5050200\begin{array} { | l | c | c | c | } \hline & \text { X-coordinate } & \text { Y-coordinate } & \text { Volume } \\\hline \text { Athens, Texas } & 30 & 30 & 150 \\\hline \text { Beaumont, Texas } & 20 & 10 & 350 \\\hline \text { Carthage, Texas } & 10 & 70 & 100 \\\hline \text { Denton, Texas } & 50 & 50 & 200 \\\hline\end{array}$

A) X = 28.125; Y = 31.25
B) X = 22000; Y = 24000
C) X = 27.5; Y = 40
D) centre of gravity = 24000
E) centre of gravity = 28

Question

East Texas Seasonings is preparing to build one processing centre to serve its four sources of seasonings. The four source locations are at coordinates shown below. Also, the volume from each source is provided. What is the centre of gravity?

5050200\begin{array} { | l | c | c | c | } \hline & \text { X-coordinate } & \text { Y-coordinate } & \text { Volume } \\\hline \text { Athens, Texas } & 30 & 30 & 150 \\\hline \text { Beaumont, Texas } & 20 & 10 & 350 \\\hline \text { Carthage, Texas } & 10 & 70 & 100 \\\hline \text { Denton, Texas } & 50 & 50 & 200 \\\hline\end{array}

A) X = 28.125; Y = 31.25
B) X = 22000; Y = 24000
C) X = 27.5; Y = 40
D) centre of gravity = 24000
E) centre of gravity = 28

Trevor Bunker · Accepted Answer

Final Answer : A, Explanation :   The center of gravity is calculated using the formula:   X = ∑ ( V o l u m e × X − c o o r d i n a t e ) ∑ V o l u m e X = \frac{\sum (Volume 	imes X-coordinate)}{\sum Volume} X = ∑ V o l u m e ∑ ( V o l u m e × X − coor d ina t e ) ​   and   Y = ∑ ( V o l u m e × Y − c o o r d i n a t e ) ∑ V o l u m e Y = \frac{\sum (Volume 	imes Y-coordinate)}{\sum Volume} Y = ∑ V o l u m e ∑ ( V o l u m e × Y − coor d ina t e ) ​  . For X:   ( 150 × 30 ) + ( 350 × 20 ) + ( 100 × 10 ) + ( 200 × 50 ) 150 + 350 + 100 + 200 = 4500 + 7000 + 1000 + 10000 800 = 22500 800 = 28.125 \frac{(150 	imes 30) + (350 	imes 20) + (100 	imes 10) + (200 	imes 50)}{150 + 350 + 100 + 200} = \frac{4500 + 7000 + 1000 + 10000}{800} = \frac{22500}{800} = 28.125 150 + 350 + 100 + 200 ( 150 × 30 ) + ( 350 × 20 ) + ( 100 × 10 ) + ( 200 × 50 ) ​ = 800 4500 + 7000 + 1000 + 10000 ​ = 800 22500 ​ = 28.125   For Y:   ( 150 × 30 ) + ( 350 × 10 ) + ( 100 × 70 ) + ( 200 × 50 ) 800 = 4500 + 3500 + 7000 + 10000 800 = 25000 800 = 31.25 \frac{(150 	imes 30) + (350 	imes 10) + (100 	imes 70) + (200 	imes 50)}{800} = \frac{4500 + 3500 + 7000 + 10000}{800} = \frac{25000}{800} = 31.25 800 ( 150 × 30 ) + ( 350 × 10 ) + ( 100 × 70 ) + ( 200 × 50 ) ​ = 800 4500 + 3500 + 7000 + 10000 ​ = 800 25000 ​ = 31.25

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