Martin 6

Martin, Kelvin, and Ahmad have 120 candies. Ahmad has six more candies than Martin. Kelvin has thrice the total amount of candies than Martin and Ahmad have. How many candies does Martin have?

Correct answer:

M =  12

Step-by-step explanation:

$$\begin{gathered} M+K+A=120 \\ A=6+M \\ K=3\cdot (M+A) \\ A+K+M=120 \\ A-M=6 \\ 3A-K+3M=0 \\ Pivot:Row1\leftrightarrow Row3 \\ 3A-K+3M=0 \\ A-M=6 \\ A+K+M=120 \\ Row2-\frac{1}{3}\cdot Row1\to Row2 \\ 3A-K+3M=0 \\ 0.333K-2M=6 \\ A+K+M=120 \\ Row3-\frac{1}{3}\cdot Row1\to Row3 \\ 3A-K+3M=0 \\ 0.333K-2M=6 \\ 1.333K=120 \\ Pivot:Row2\leftrightarrow Row3 \\ 3A-K+3M=0 \\ 1.333K=120 \\ 0.333K-2M=6 \\ Row3-\frac{0.33333333}{1.33333333}\cdot Row2\to Row3 \\ 3A-K+3M=0 \\ 1.333K=120 \\ -2M=-24 \\ M=\frac{-24}{-2}=12 \\ K=\frac{120}{1.33333333}=90 \\ A=\frac{0+K-3M}{3}=\frac{0+90-3\cdot 12}{3}=18 \\ A=18 \\ K=90 \\ M=12 \end{gathered}$$

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