Bill owns a large collection of fishing lures consisting of small, medium, and large lures that weigh 3, 4, and 5 grams each, respectively. If the product of the lure weights that Bill sold to his friend is 216,000 grams, how many medium lures did he sell?
","rationale_html":"first step:
216,000 = 216 * 1000
1000 = 10^3 or 5^3 * 2^3.
216 = 2 * 108 = 2*2* 54
54 = 2*27 = 2*3^3.
total, we have:
2^3(from 1000) * 5^3(from 1000) * 2^3(from 216) * 3^3(from 2016)
combine:
2^6 * 5^3 * 3^3
we can rewrite 2^6 as 4^3.
since we are asked for the exponent for 4,
C
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