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?

Correct answer:

a =  50
b =  60

Step-by-step explanation:

a:b=5:6 (a−10):(b+10) = 4:7  a=65​⋅ b a−10=74​⋅ (b+10)  a=5/6⋅ b a−10=4/7⋅ (b+10)  6a−5b=0 7a−4b=110  Pivot:Row1↔Row2 7a−4b=110 6a−5b=0  Row2−76​⋅ Row1→Row2 7a−4b=110 −1.57b=−94.29  b=−1.57142857−94.28571429​=60 a=7110+4b​=7110+4⋅ 60​=50  a=50 b=60

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