Dual increases

The two numbers are in the ratio of 5:6. If the first one decreases by ten, and the second one increases by ten, then these two numbers are in the ratio of 4:7. What are the numbers?

Final Answer:

a =  50
b =  60

Step-by-step explanation:

$$\begin{gathered} a:b=5:6 \\ (a-10):(b+10)=4:7 \\ a=\frac{5}{6}\cdot b \\ a-10=\frac{4}{7}\cdot (b+10) \\ a=5/6\cdot b \\ a-10=4/7\cdot (b+10) \\ 6a-5b=0 \\ 7a-4b=110 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{6}{7}\cdot Row1\to Row2 \\ -1.57b=-94.29 \\ b=\frac{-94.28571429}{-1.57142857}=60 \\ a=\frac{110+4b}{7}=\frac{110+4\cdot 60}{7}=50 \\ a=50 \\ b=60 \end{gathered}$$

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