SOLUTION: 6. Gary hung seven strings of holiday lights on his house. Some strings had 75 lights and the rest had 100 lights per string. When a fuse blew. One-third of the lights went out

Question 30014: 6. Gary hung seven strings of holiday lights on his house. Some strings had 75 lights and the rest had 100 lights per string. When a fuse blew. One-third of the lights went out but 400 lights still worked. How many of the seven strings had 75 lights?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Gary hung seven strings of holiday lights on his house.
x = # strings with 75 lights
7 - x = # strings with 100 lights
75x + 100(7 - x) = 400 + (75x + 100(7-x))/3
3(75x + 100(7-x)) = 1200 + 75x + 100(7 - x)
225x + 300(7 - x) = 1200 + 75x + 100(7 - x)
225x + 200(7 - x) = 1200 + 75x
150x + 1400 -200x = 1200
-50x + 1400 = 1200
-50x = -200
x = 4
7 - x = 3
There are 4 strings with 75 lights and 3 strings with 100 lights
check
75*4 + 100(7 - 4) = 400 + (75*4 + 100(7-4))/3
300 + 300 = 400 + (300 + 300)/3
600 = 400 + 200
600 = 600
OK
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