1. **State the problem:** A street vendor has 360 T-shirts total, some short sleeve and some long sleeve. Short sleeve shirts sell for 14 each, long sleeve for 16 each. Total sales amount to 5420. We need to find how many of each type were sold. 2. **Define variables:** Let $x$ = number of short sleeve shirts, $y$ = number of long sleeve shirts. 3. **Write equations:** - Total shirts: $$x + y = 360$$ - Total sales: $$14x + 16y = 5420$$ 4. **Solve the system:** From the first equation, express $y$: $$y = 360 - x$$ 5. Substitute into the sales equation: $$14x + 16(360 - x) = 5420$$ 6. Distribute: $$14x + 5760 - 16x = 5420$$ 7. Combine like terms: $$\cancel{14x} - \cancel{16x} = -2x$$ $$-2x + 5760 = 5420$$ 8. Subtract 5760 from both sides: $$-2x = 5420 - 5760$$ $$-2x = -340$$ 9. Divide both sides by -2: $$x = \frac{-340}{-2} = 170$$ 10. Find $y$: $$y = 360 - 170 = 190$$ **Answer:** The vendor sold 170 short sleeve T-shirts and 190 long sleeve T-shirts.