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

#1**+1 **

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**+1 **

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**

** !**

asinus
Jun 5, 2017