Math test question

Question

On a certain test there are two types of questions – multiple choice questions worth 2 marks each and short answer questions that are worth 5 marks each. The test is out of a total of 64 marks. How many of each type of question are there on the test if there are one and a half times as many multiple choice questions as short answer questions?

Answer 1

let number of Qs of 5 marks = x

total marks of these Qs = 5x

No of 2 marks Qs 1 1/2 times more = 3/2 x

marks of these Qs = 2 • 3/2 x = 3x∴

∴ 5x + 3x = 64

8x = 64

x = 8 ∴

∴ 8 Qs of 5 marks = 40 marks

12 Qs of 2 marks = 24

∴ Total marks = 64