+16 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?
+21 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.
