1. **State the problem:** Bonaficio sells thingamabobs and whosie-whats-its. He sold 12 thingamabobs and 10 whosie-whats-its for 111.20, and another shipment of 10 thingamabobs and 15 whosie-whats-its for 124.40. We need to find the cost of each item. 2. **Identify variables:** Let $x$ = cost of one thingamabob Let $y$ = cost of one whosie-whats-it 3. **Write the system of equations:** $$10x + 15y = 124.40$$ $$12x + 10y = 111.20$$ 4. **Solve the system using elimination:** Multiply the first equation by 2 and the second by 3 to align coefficients of $y$: $$20x + 30y = 248.80$$ $$36x + 30y = 333.60$$ 5. **Subtract the first new equation from the second:** $$(36x + 30y) - (20x + 30y) = 333.60 - 248.80$$ $$16x = 84.80$$ 6. **Solve for $x$:** $$x = \frac{84.80}{16} = 5.30$$ 7. **Substitute $x=5.30$ into the first original equation:** $$10(5.30) + 15y = 124.40$$ $$53 + 15y = 124.40$$ $$15y = 124.40 - 53 = 71.40$$ 8. **Solve for $y$:** $$y = \frac{71.40}{15} = 4.76$$ **Final answer:** The cost of one thingamabob is $5.30$ and one whosie-whats-it is $4.76$.