jcherry99

Answer:

Step-by-step explanation:

You pretty much have to do A, to get at B.

This is what is called a Diophantine equation. The answer much be a whole number. So we'll set one of the conditions up. There's not much room to move around to get the first answer.

Equations

Let x be the number of 2 point questions.

Let y be the number of 1/2 deductions.

Let z be the number of questions that are not answered.

Solutions

z = 0 (All questions are answered)

x + y = 50  

2x - 1/2 y = 80   Multiply this equation by 2

4x - y = 160        Add the first equation to this one.

x  + y =  50

5x =     210         Divide by 5

5x/5 = 210/5      Do the division

x = 42

x + y = 50               Substitute x = 42 into this equation

42 +  y = 50           Subtract 42 from both sides

42-42 + y = 50-42  Do the subtraction

y = 8

One solution is x=42 and y = 8

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I can find no other solutions that will work. If he can get over 80 then if he answers 44 correctly and leaves the rest blank, his mark is 88

If he answers 43 correctly and leaves the rest blank is mark is 86

If he answers 45 and leaves 5 blank, his mark is ninety. In each case, he doesn't get any wrong.