Question

A student is taking a test in which items of type A are worth 8 points and items of type B are worth 12 points. It takes 3 min to complete each item of type A and 6 min to complete each item of type B. The total time allowed is 60 min and Anna answers exactly 16 questions. How many questions of each type did she complete? Assuming that all her answers were correct, what was her score? She completed questions of type A.

Answer 1

Type A questions are worth 8 points each.

Type B questions are worth 12 points each.

it takes 3 minutes to answer a Type A question

it takes 6 minutes to answer a Type B question.

total time allowed = 60 minutes

She answered a total of 16 questions.

let

number of question answer on type A = x

number of question answered on type B = y

Therefore,

3x + 6y = 60

x + y = 16

then,

`\begin{gathered} 3x+6y=60 \\ x+y=16 \\ x=16-y \\ 3(16-y)+6y=60 \\ 48-3y+6y=60 \\ 3y=60-48 \\ 3y=12 \\ y=(12)/(3) \\ y=4 \\ x=16-4 \\ x=12 \end{gathered}`

She answered 12 questions on type A and 4 questions on type B.

If all her answer is correct her score can be computed below