Multiple Choice Algebra Question

Question

Tommy completed a multiple choice test with 40 questions. Each correct answer was worth 4 marks and 1 mark was subtracted for each incorrect answer. Tommy scored 120 marks. Set up a pair of simultaneous equations and solve them to find the number of questions he got correct

Answer 1

Let x = the number of questions Tommy answered correctly and y = the number he got wrong.

 

There were 40 questions:

• x + y = 40

Each correct answer was worth 4 marks and 1 mark was subtracted for each incorrect answer. Tommy scored 120 marks:

• 4*x - 1*y = 120

 

To solve, add the two equations:

 

 x + y =   40

4x - y = 120

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5x + 0 = 160

 

5x = 160

x = 32

 

To find y, plug x = 32 into either original equation and solve for y:

 

x + y = 40

32 + y = 40

y = 8