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At the Bubble Gum Factory, lengths of gum are stretched to larger…

January 26, 2024

At the Bubble Gum Factory, lengths of gum are stretched to larger lengths by putting them through stretching machines. There are 100 stretching machines, numbered 1 through 100. Machine 1 does nothing to a piece of gum; machine 2 stretches pieces of gum to twice their original length; machine 3 triples the length of gum, and so forth. So, machine 23, for example, will stretch a piece of gum to 23 times its original length.

An order has just come in for a piece of bubble gum 26 inches in length. The factory has pieces of gum that are only 1 inch long, and machine number 26 is broken. Is there any way to create a piece of bubble gum 26 inches in length using other machines?

Some of the machines in the factory are unnecessary because combinations of others machines could be used instead. Figure out which machines are actually unnecessary.

Algebra, Bubble, factory, gum, larger.., lengths, stretched

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