Algebra 1 word problem; translate and solve. Answer included.

Question

in a recent survey, 2/3 of the lions said that they were happy to serve as king of the forest, while another 1/9 thought it was way too much responsibility. if 14 lions gave one of these two answers, how many lions were surveyed in total?

Correct answer is 18Lions.

How did they translate this into something that came out to 18?

Answer 1

Here's what we know:

²/₃ x + ¹/₉ x = 14 (2/3 of the surveyed plus another 1/9 total 14)

find the LCD to add together:

⁶/₉ x + ¹/₉ x = 14

Simplify:

⁷/₉ x = 14

Multiply both sides by 9/7:

x = 14 * ⁹/₇

Factor out 7:

x = 2 * 9

Multiply

x = 18