Mathematics 7806

Janko has committed that his average grade in mathematics will be exactly 2 at the end of the semester. However, so far, he has received grades 3 and 4. He knows that by the end of the year, he will receive four more grades from the tests. What are the worst grades he can get to meet his goal?

Correct answer:

z =  2

Step-by-step explanation:

$$\begin{gathered} (a+b+c+d+3+4)/(4+2)=2 \\ a+b+c+d+7=12 \\ a+b+c+d=5 \\ 1+1+1+2=5 \\ z=2 \end{gathered}$$

The equations have the following integer solutions:

(a+b+c+d+3+4)/(4+2)=2
a>0
b>0
c>0
d>0

Number of solutions found: 4

a₁=1, b₁=1, c₁=1, d₁=2
a₂=1, b₂=1, c₂=2, d₂=1
a₃=1, b₃=2, c₃=1, d₃=1
a₄=2, b₄=1, c₄=1, d₄=1

Calculated by our Diofant problems and integer equations.

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