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Cindy had some decorative lights. She used \( {1 \over 3}{}{}\) of the decorative lights for 12 small Christmas trees. She used \( {3 \over 4}{}{}\)of the remaining decorative lights for 10 big Christmas trees. Given that each big Christmas tree had 16 more decorative lights than each small Christmas tree, how many decorative lights did Cindy have at first?

 Sep 14, 2021
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x = number of lights             s = small tree lights               L = large tree  = s+16

 

1/3 x  =  12 s    or s = 1/36 x        (now there are 2/3 x lights left)

       and 

(2/3x) 3/4 = 10 (s+16)         sub in the green equation for s

1/2 x = 10(1/36 x + 16)

x = 720 lights

 Sep 14, 2021

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