Subjects algebra

Pencils Pens 1Adb5D

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** You spent 11 on pencils and pens. Pencils cost 0.25 each, pens cost 2 each, and you bought a total of 30 items. 2. **Define variables:** Let $x$ be the number of pencils and $y$ be the number of pens. 3. **Write the system of equations:** - Total items: $$x + y = 30$$ - Total cost: $$0.25x + 2y = 11$$ This matches option C. 4. **Solve for the number of pencils:** From the first equation, express $y$: $$y = 30 - x$$ Substitute into the cost equation: $$0.25x + 2(30 - x) = 11$$ 5. **Simplify and solve:** $$0.25x + 60 - 2x = 11$$ $$60 - 1.75x = 11$$ 6. **Isolate $x$:** $$-1.75x = 11 - 60$$ $$-1.75x = -49$$ 7. **Divide both sides by -1.75:** $$x = \frac{-49}{-1.75}$$ Show cancellation: $$x = \frac{\cancel{-49}}{\cancel{-1.75}} = 28$$ 8. **Interpretation:** You bought 28 pencils. **Final answer:** 28 pencils.