PROBLEM SET Solve the following problems using inductive or deductive reasoning. Show your solutions. You may use any approach or strategy for as long as it is mathematically sound. 1. On a balance scale, two spools and one thimble balance eight buttons. Also, one spool balances one thimble and a button. How many buttons will balance one spool? 2. Every GOOP is a GORP. Half of all GORGS are GORPS. Half of all GORPS are GOOPS. There are 40 GORGS and 30 GOOPS. No GORG is a GOOP. How many GORPS are neither GOOPS nor GORGS?

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