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?
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
+14903 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
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