1. **State the problem:** A company buys inkjet printers, LCD monitors, and memory chips. Total items bought: 41. Costs: printer = 113, monitor = 137, memory chip = 93. Total cost: 4457. Memory chips are twice the number of monitors. Find how many of each were purchased. 2. **Define variables:** Let $x$ = number of inkjet printers, $y$ = number of LCD monitors, $z$ = number of memory chips. 3. **Write the system of equations:** From the problem: - Total cost: $$113x + 137y + 93z = 4457$$ - Total items: $$x + y + z = 41$$ - Memory chips twice monitors: $$z = 2y$$ 4. **Substitute $z = 2y$ into the total items equation:** $$x + y + 2y = 41$$ $$x + 3y = 41$$ 5. **Substitute $z = 2y$ into the cost equation:** $$113x + 137y + 93(2y) = 4457$$ $$113x + 137y + 186y = 4457$$ $$113x + 323y = 4457$$ 6. **Solve the system:** From step 4: $$x = 41 - 3y$$ Substitute into step 5: $$113(41 - 3y) + 323y = 4457$$ $$4633 - 339y + 323y = 4457$$ $$4633 - 16y = 4457$$ $$-16y = 4457 - 4633$$ $$-16y = -176$$ $$y = \frac{-176}{-16} = 11$$ 7. **Find $x$ and $z$:** $$x = 41 - 3(11) = 41 - 33 = 8$$ $$z = 2y = 2(11) = 22$$ **Answer:** The company purchased 8 inkjet printers, 11 LCD monitors, and 22 memory chips.