Domino

Domino and Winnie share some biscuits. The ratio of biscuits between them was 4:3. Domino gave Winnie 5 biscuits, and the ratio changed to 1:2. How many biscuits are in total?

Correct answer:

x =  21

Step-by-step explanation:

$$\begin{gathered} a:b=4:3 \\ (a-5):(b+5)=1:2 \\ 3a=4b \\ 2\cdot (a-5)=1\cdot (b+5) \\ 3\cdot a=4\cdot b \\ 2\cdot (a-5)=1\cdot (b+5) \\ 3a-4b=0 \\ 2a-b=15 \\ Row2-\frac{2}{3}\cdot Row1\to Row2 \\ 3a-4b=0 \\ 1.67b=15 \\ b=\frac{15}{1.66666667}=9 \\ a=\frac{0+4b}{3}=\frac{0+4\cdot 9}{3}=12 \\ a=12 \\ b=9 \\ x=a+b=12+9=21 \end{gathered}$$

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