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.
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}.
the answer was incorrect
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}.