Ratio of two unknown numbers

Two numbers are hidden. Their sum is 30. We calculate one-sixth of a larger number and add to both numbers. So we get new numbers whose ratio is 5:7. Which two numbers is it?

Correct answer:

a =  12
b =  18

Step-by-step explanation:


a+b=30
a+(b/6) = 5/7 ·(b+b/6)

a+b = 30
42a-28b = 0

Pivot: Row 1 ↔ Row 2
42a-28b = 0
a+b = 30

Row 2 - 1/42 · Row 1 → Row 2
42a-28b = 0
1.67b = 30


b = 30/1.66666667 = 18
a = 0+28b/42 = 0+28 · 18/42 = 12

a = 12
b = 18

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