청심국제중학교 (경기 가평군) 중등2 2023 2학기 중간

1. 1.

   1. Which linear system has the solution $x=5$ and $y=6$? [3.0] ```choices - $0.2x + 0.5y = 4$ $\frac{1}{3}x - \frac{1}{5}y = -1$ - $0.2x + 0.5y = -4$ $\frac{1}{5}x - \frac{1}{3}y = 1$ - $0.2x + 0.5y = 4$ $\frac{1}{5}x - \frac{1}{3}y = -1$ - $-0.2x + 0.5y = 4$ $-\frac{1}{5}x - \frac{1}{3}y = -1$ - $0.2x + 0.5y = -4$ $\frac{1}{5}x + \frac{1}{3}y = 1$ ```

2. 2.

   Create a linear system to model this situation [3.0] A woman is 5 times as old as her daughter. In 20 years, she will be 2 times as old as her daughter will be. ```choices - $a=5b$ $2a+20=b+20$ - $a=5+b$ $20a=2(20b)$ - $a=5b$ $a-20=2(b-20)$ - $a=5b$ $a+20=2(b+20)$ ```

3. 3.

   Two phone billing companies determine their prices using different formulas Company A: $p=3c+27$ Company B: $p=3.75c+12$ where $p$ represents the phone billing, and $c$ represents the calling time. Solve to determine at what calling time both companies charge the same price. ```choices - $p=57\n\;\;c=20$ - $p=87\n\;\;c=20$ - $p=47\n\;\;c=10$ - $p=72\n\;\;c=35$ - $p=68\n\;\;c=15$ ```

4. 4.

   4. Flying to Jeju with a tailwind a plane averaged $158$ km/h. On the return trip the plane only averaged $112$ km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air. [3.0] ```choices - plane : $145$ km/h, wind : $23$ km/h - plane : $135$ km/h, wind : $23$ km/h - plane : $135$ km/h, wind : $33$ km/h - plane : $125$ km/h, wind : $23$ km/h - plane : $100$ km/h, wind : $58$ km/h ```

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