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When a certain pot is filled with cream of mushroom soup, it weighs 19 kg. When it is filled with clear chicken broth, it weighs 9 kg. If the cream of mushroom soup is 3 times as heavy as the clear chicken broth, how heavy is the pot?

Guest Jun 5, 2017
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2+0 Answers

 #1
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Let the weight of the pot =P

Let the weight of the clear chicken broth =C

 

P + C  = 9, and 

P + 3C =19, solve for C, P

 

Solve the following system:
{C + P = 9 | (equation 1)
3 C + P = 19 | (equation 2)
Swap equation 1 with equation 2:
{3 C + P = 19 | (equation 1)
C + P = 9 | (equation 2)
Subtract 1/3 × (equation 1) from equation 2:
{3 C + P = 19 | (equation 1)
0 C+(2 P)/3 = 8/3 | (equation 2)
Multiply equation 2 by 3/2:
{3 C + P = 19 | (equation 1)
0 C+P = 4 | (equation 2)
Subtract equation 2 from equation 1:
{3 C+0 P = 15 | (equation 1)
0 C+P = 4 | (equation 2)
Divide equation 1 by 3:
{C+0 P = 5 | (equation 1)
0 C+P = 4 | (equation 2)
Collect results:
Answer: | C = 5        and               P = 4

Guest Jun 5, 2017
 #2
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When a certain pot is filled with cream of mushroom soup, it weighs 19 kg. When it is filled with clear chicken broth, it weighs 9 kg. If the cream of mushroom soup is 3 times as heavy as the clear chicken broth, how heavy is the pot?

 

I.           p+com=19kg

II.            p+ccb=9kg

III.             com=3ccb

 

III. in I. p+3ccb =19kg

II.         p + ccb = 9kg

diff.          2ccb = 10kg

/ 2              ccb = 5kg

                    

II             p+5kg=9kg

- 5kg

                      p=4kg

 

The pot weighs 4kg

 

laugh  !

asinus  Jun 5, 2017

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