which number should be added to -7/8 so that it becomes 5/9
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Let x and y be the numbers in the ratio 5:9. By symmetry, x/y = 5/9 -> 5y=9x and y=9/5 x. We will use this expression later to solve for x.
Add 9 to both numbers, x+9 : y+9 = 16:27. Or (x+9)/(y+9) = 16/27.
16(y+9) = 27(x+9) -> 16y+144 = 27x + 243. Now, we substitute y= 9/5 x to the LHS.
16(9/5)x +144 = 27x +243. Simplify the LHS: 144x/5 +144 = 27x +243, which simplifies to 28.8x - 27x = 99. So 1.8x or 9/5 x = 99 -> 9x=495 and x = 55.
Substitute x=55 in the equation 5y=9x. 5y = 9x55 or 495 -> y=99 - this is the second number given in the list.
Check the ratios. 55:99 simplifies to 5:9. Add 9 to both numbers: 64:108 simplifies to 16:27……poc
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