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?

Answer: Bill sold 3 medium lures.

Step-by-step explanation:

We let the number of small lures be S, the number of medium lures be M and number of large lures be L.

Now the product of weights of lure is expressed as 3^S*4^M * 5^L

Since we are told that the weight product is equal to 216,000. Now we have 216,000 = 3^S*4^M * 5^L.

Ours to do is get the unknown exponents such that the product is 216,000.

By using the factorization method we find that 216,000 = 3^3 * 4^3 * 5^3

Therefore M = 3

Bill sold 3 medium lures.

Step-by-step explanation:

The medium lures are 4 grams and he sold 216 000 grams

Therefore

216 000 (amount he sold) : 4 grams (weight of medium lures) = 54 000 lures