In an examination one mark is awarded for every correct answer while 1

1.	In an examination one mark is awarded for every correct answer while 1/4 mark is deducted for every wrong answer. A student answered 200 question and got 125 marks. Represent this situation algebraic ally and graphically.
Answer» let the CORRECT ANSWER be X and let the WORNG answer be y now, $:\implies\sf \: x + y = 120 ---- (1) \\ \\ \\:\implies\sf \: 1 \times x - \frac{1}{4} \times y = 90 \\ \\ \\ :\implies\sf \: x - \frac{1}{4} \: \: y = 90 \times y \\ \\ \\$ $:\implies\sf 4x - \cancel4 \times \frac{1}{ \cancel4}y = 360 \\ \\ \\ :\implies\sf \: 4x - \cancel y = 360 - - - - (2) \\ \\ \\ :\implies\sf \: x + y = 120(from \: 1 \: equation) \\ \\ \\$ $:\implies\sf \: 5x = 480 \\ \\ \\ :\implies\sf \: \cancel \frac{480}{5} = x \\ \\ \\ :\implies\sf \: x = 96 \\ \\$ so therefore no.of correct answer are 96 $\\$

In an examination one mark is awarded for every correct answer while 1/4 mark is deducted for every wrong answer. A student answered 200 question and got 125 marks. Represent this situation algebraic ally and graphically.

Answer»

and let the WORNG answer be y

now,

$:\implies\sf \: x + y = 120 ---- (1) \\ \\ \\:\implies\sf \: 1 \times x - \frac{1}{4} \times y = 90 \\ \\ \\ :\implies\sf \: x - \frac{1}{4} \: \: y = 90 \times y \\ \\ \\$

$:\implies\sf 4x - \cancel4 \times \frac{1}{ \cancel4}y = 360 \\ \\ \\ :\implies\sf \: 4x - \cancel y = 360 - - - - (2) \\ \\ \\ :\implies\sf \: x + y = 120(from \: 1 \: equation) \\ \\ \\$