Question
in a recent survey, 2/3 of the lions said they would be happy to serve as king of the forest, while another 1/9 thought it was way too much of a responsibility. If 14 lions gave one of these two answers, how many lions were surveyed in total? make sure your answer is fully reduced.
Answers
Answer
the answer was incorrect
Answered by
GPT 3.5
Let's use L to represent the total number of lions surveyed.
According to the survey, 2/3 of the lions said they would be happy to serve as king of the forest, which means (2/3)L lions gave this answer.
Another 1/9 of the lions thought it was way too much responsibility, which means (1/9)L lions gave this answer.
The total number of lions who gave either of these two answer is given as 14. So, we can set up the equation:
(2/3)L + (1/9)L = 14
Multiplying through by 9 to remove the fractions, we get:
(6/3)L + (1/3)L = 126
(7/3)L = 126
Multiplying through by 3 to eliminate the fraction, we get:
7L = 378
Dividing both sides by 7, we get:
L = 378/7
L = 54
Therefore, there were a total of 54 lions surveyed. Answer: \boxed{54}.
According to the survey, 2/3 of the lions said they would be happy to serve as king of the forest, which means (2/3)L lions gave this answer.
Another 1/9 of the lions thought it was way too much responsibility, which means (1/9)L lions gave this answer.
The total number of lions who gave either of these two answer is given as 14. So, we can set up the equation:
(2/3)L + (1/9)L = 14
Multiplying through by 9 to remove the fractions, we get:
(6/3)L + (1/3)L = 126
(7/3)L = 126
Multiplying through by 3 to eliminate the fraction, we get:
7L = 378
Dividing both sides by 7, we get:
L = 378/7
L = 54
Therefore, there were a total of 54 lions surveyed. Answer: \boxed{54}.
Answered by
GPT 3.5
Apologies for the mistake. Let's solve it again.
Let x be the total number of lions surveyed.
According to the survey, 2/3 of the lions said they would be happy to serve as king of the forest, which means (2/3)x lions gave this answer.
Another 1/9 of the lions thought it was way too much responsibility, which means (1/9)x lions gave this answer.
The total number of lions who gave either of these two answers is given as 14. So, we can set up the equation:
(2/3)x + (1/9)x = 14
Multiplying both sides of the equation by 9 to eliminate the fraction, we get:
6x + x = 126
Combine like terms:
7x = 126
Divide both sides by 7:
x = 126/7
x = 18
Therefore, the total number of lions surveyed is 18. Answer: \boxed{18}.
Let x be the total number of lions surveyed.
According to the survey, 2/3 of the lions said they would be happy to serve as king of the forest, which means (2/3)x lions gave this answer.
Another 1/9 of the lions thought it was way too much responsibility, which means (1/9)x lions gave this answer.
The total number of lions who gave either of these two answers is given as 14. So, we can set up the equation:
(2/3)x + (1/9)x = 14
Multiplying both sides of the equation by 9 to eliminate the fraction, we get:
6x + x = 126
Combine like terms:
7x = 126
Divide both sides by 7:
x = 126/7
x = 18
Therefore, the total number of lions surveyed is 18. Answer: \boxed{18}.
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