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This problem trains for: SAT-I, AMC-8, GMAT, Math Kangaroo 5-6, Math Kangaroo 7-8.

In a tree bark ecosystem 15% of the population of Arthropods are Arachnids and 11% are Coleopterans. Approximately what percentage of the number of Arachnids does the number of Coleopterans represent?

Let us denote the number of Arachnids with A, the number of Coleopterans with C and the total number of Arthropods with N.

Then, we have that:

equation

equation

and we have to find x such that:

equation

We solve for N in the first relation and substitute in the second:

equation

equation

equation

We solve for x, the unknown percentage:

equation