Numbers at ratio 2

Two numbers are in the ratio 3:5. If each number is increased by 10, the ratio becomes 5:7. Find the sum of the numbers.

Correct answer:

s =  40

Step-by-step explanation:

a:b=3:5 (a+10):(b+10)=5:7  5a=3b 7(a+10)=5(b+10)  5⋅ a=3⋅ b 7⋅ (a+10)=5⋅ (b+10)  5a−3b=0 7a−5b=−20  Pivot:Row1↔Row2 7a−5b=−20 5a−3b=0  Row2−75​⋅ Row1→Row2 7a−5b=−20 0.57b=14.29  b=0.5714285714.28571429​=25 a=7−20+5b​=7−20+5⋅ 25​=15  a=15 b=25  s=a+b=15+25=40

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