Roger had some faily lights. He used 1/3 of the fairy lights to decorate15 small Christmas trees and 2/5 of the fairy lights to decorate 6 big Christmas trees. He kept the rest. Each big Christmas tree had 14 more fairy lights than each small Christmas tree. How many fairy lights did Roger have at first?
Roger used 15 small Christmas trees * 14 fairy lights/small Christmas tree = 210 fairy lights on small Christmas trees.
The 6 big Christmas trees each had 14 fairy lights/small Christmas tree + 14 fairy lights = 28 fairy lights.
In total, Roger used 210 fairy lights + 6 * 28 fairy lights = 278 fairy lights.
If Roger used 1/3 of the fairy lights to decorate the small Christmas trees, he had 3 * 278 fairy lights = 834 fairy lights at first.
So the answer is 834
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L - 1/3L = 2/3L left
2/3L - 2/5L =4/15L left unused.
1/3 L / 15=1/45L - fairy lights per small christmas tree
2/5L / 6 =1/15L - fairy lights per large Xmas tree.
1/15L=1/45L + 14, solve for L
L =315 fairy lights - what Roger had at first.
Check: [315 * 1/45] = 7 fairy lights for each small Xmas tree
[315 * 1/15 ] = 21 fairy lights for each large Xmas tree
[315 * 4/15] = 84 fairy light left unused + [7 * 15] + (6 * 21] =315 fairy light at first.