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Two numbers are in the ratio 8: 9 . If 6 is subtracted from each, the ratio becomes 5: 6
find the numbers.
Given: Two numbers are in the ratio 8: 9. If 6 is subtracted from each, the ratio becomes 5: 6
To do: Find the numbers
Solution:
Two numbers are in the ratio $ 8 : 9$
so, the numbers are $8 x$ and $9 x$
If 6 is subtracted from each number then it becomes 5 : 6
$\frac{8 x - 6}{9 x - 6} = \frac{ 5}{ 6}$
Cross multiply
$(8 x - 6)\times 6 = 5 \times (9 x -6)$
Multiply the numbers inside the brackets,
$48 x - 36 = 45 x - 30$
$48 x - 45 x = -30 + 36$ (keep variables on one side and numbers on the other side)
$3 x = 6$
$x = \frac{6}{ 3}$
$x = 2$
Therefore the numbers are,
$8 (2) : 9 (2)$
$16 : 18$
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