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0
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FIll in the boxes

Aug 3, 2020

#1
+25543
+2

My attempt:

$$\begin{array}{|rcl|l|} \hline 1 &:& 3 & \\ a &:& a+c & c \\ \hline 1 &:& 3 & 3-1 = 2 & \text{yes } \\ 2 &:& 6 & 6-2 = 4 & \text{yes } \\ 3 &:& 9 & 9-3 = 6 & \text{yes } \\ 4 &:& 12 & 12-4 = 8 & \text{yes } \\ \hline 5 &:& 15 & 15-5 = 10 & \text{no } \ c\ge10 \\ \vdots &:& \vdots & \vdots & \text{no } \ c\ge10 \\ \hline \end{array}$$ $$\ldots \text{ so } \mathbf{a=\{1,2,3,4\} }$$

$$\begin{array}{|rcl|l|} \hline 3 &:& 5 & \\ a &:& a+b & b \\ \hline \mathbf{\color{red}3} &:& 5 & 5-3 = \mathbf{\color{red}2} & \text{yes } \\ \hline 6 &:& 10 & 10-6 = 4 & \text{no } \ a\ne \{1,2,3,4\} \\ \vdots &:& \vdots & \vdots & \text{no } \ a\ne \{1,2,3,4\} \\ \hline \end{array}$$$$\ldots \text{ so } \mathbf{a=3} \ \rightarrow \ \mathbf{b=2}\ \rightarrow \ \mathbf{c=6}$$

$$\begin{array}{|rcll|} \hline \mathbf{ 50\%*(b+d)} &=&\mathbf{ b } \\ 50\%* b+ 50\%*d &=& 100\% *b \\ 50\%*d &=& 100\% *b-50\% *b \\ 50\%*d &=& 50\%* b \\ d &=& b \quad | \quad \mathbf{b=2} \\ \mathbf{ d } &=& \mathbf{ 2 } \\ \hline \end{array}$$

check:

$$\dfrac{1}{3} * (3+6) = 3 \ (a=3\checkmark) \\~\\ \dfrac{1}{2} * (2+2) = 2 \ (d=2\checkmark)\\~\\ \dfrac{3}{5} * (3+2) = 3 \ (a=3\checkmark)\\~\\ \dfrac{1}{4} * (6+2) = 2 \ (d=2\checkmark)$$

Aug 3, 2020