Write this information as two simultaneous equations

Question

In an examination there are several short questions worth 2 marks and some long ones worth 5 marks each. The answer to any question is either right and given full marks or wrong and given zero. Rajinder gets 70 marks from 17 correct answers

Answer 1

Let x be the number of 2 mark questions, y be the number of 5 mark questions.

1) x + y = 17 or x = 17 - y

2) 2x + 5y = 70

substitute eq(1) into eq(2):

2(17 - y) + 5y = 70

34 - 2y + 5y = 70

3y = 36

y = 12

using eq(1):

x = 17 - 12 = 5

check using eq(2):

2(5) + 5(12) = 70

10 + 60 = 70

70 = 70

Rajinder correctly answered 5 two point questions and 12 five point questions.