Practise the method.
Example 1
A quiz has 28 questions: correct answers earn 3 points, wrong answers lose 2, blanks score 0. A student leaves 6 blank and scores 36. How many answers were correct?
Show worked answer
Answer: 16
- There were 22 attempted answers.
- If c were correct, 22−c were wrong.
- Solve 3c−2(22−c)=36, giving c=16.
Example 2
A balance starts at−$17. Every day $6 is deposited and a $4 fee is deducted. For how many whole numbers of days d≥0 is the resulting balance at least $3 but less than $20?
Show worked answer
Answer: 9
- The balance after d days is−17+2d.
- Solve 3≤−17+2d<20
- count the whole-number days between its bounds.
Example 3
A quiz has 23 questions: correct answers earn 6 points, wrong answers lose 2, blanks score 0. A student leaves 3 blank and scores 56. How many answers were correct?
Show worked answer
Answer: 12
- There were 20 attempted answers.
- If c were correct, 20−c were wrong.
- Solve 6c−2(20−c)=56, giving c=12.