SOLUTION: Eleven groups of people were checking into a hotel. Group one made up 1/4 of the total number of people. Group two made up 2/6 of the total number of people. Group three made up 1/

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Eleven groups of people were checking into a hotel. Group one made up 1/4 of the total number of people. Group two made up 2/6 of the total number of people. Group three made up 1/      Log On


   

Question 180812: Eleven groups of people were checking into a hotel. Group one made up 1/4 of the total number of people. Group two made up 2/6 of the total number of people. Group three made up 1/8 the total number of people. Group four made up 1/12 the total number of people. Group five made up 1/32 the total number of people. Group six made up 1/24 the total number of people. Group seven made up 1/16 the total number of people. Group eight made up 1/64 the total number of people. Group nine made up 1/64 the total number of people. Group ten made up 1/48 the total number of people. Group eleven consisted of 240 people. What was the total number of rooms needed if each room could be occupied by just one person?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Eleven groups of people were checking into a hotel. Group one made up 1/4 of the total number of people. Group two made up 2/6 of the total number of people. Group three made up 1/8 the total number of people. Group four made up 1/12 the total number of people. Group five made up 1/32 the total number of people. Group six made up 1/24 the total number of people. Group seven made up 1/16 the total number of people. Group eight made up 1/64 the total number of people. Group nine made up 1/64 the total number of people. Group ten made up 1/48 the total number of people. Group eleven consisted of 240 people. What was the total number of rooms needed if each room could be occupied by just one person?
:
let x = total number rooms required
:
1%2F4x + 2%2F6x + 1%2F8x + 1%2F12x + 1%2F32x + 1%2F24x + 1%2F16x + 1%2F64x + 1%2F64x + 1%2F48x + 240 = x
Find the least common multiple of 64 & 48
64: 2*2*2*2*2*2
48: 2*2*2*2*3
2*2*2*2*2*2*3 = 192, multiply equation by the LCM to get rid of the denominators
192*1%2F4x + 192*2%2F6x + 192*1%2F8x + 192*1%2F12x + 192*1%2F32x + 192*1%2F24x + 192*1%2F16x + 192*1%2F64x +
192*1%2F64x + 192*1%2F48x + 192(240) = 192(x)
:
Results of canceling the denominators:
48x + 32(2x) + 24x + 16x + 6x + 8x + 12x + 3x + 3x + 4x + 46080 = 192x
48x + 64x + 24x + 16x + 6x + 8x + 12x + 3x + 3x + 4x + 46080 = 192x
188x + 46080
188x - 192x = -46080
-6x = -46080
x = %28-46080%29%2F%28-6%29
x = 7,680 rooms required
;
A lot of math here, check my work.