Answer: it will increase by 200%
Step-by-step explanation:
Lets call the original fraction x/y
and lets call the amount it was increased by a
which means that x/y multiplied by a = 0.9x/0.3y
because the numerator decreased by 10% and the denominator decreased by 70%
because of this you get the equation x/y * a = 0.9x/0.3y
you get xa/y= 0.9x/0.3y
you cross multiply and get the equation 0.3yxa=0.9yx
you cancel the yx from both sides and you're left with 0.3a=0.9
you solve the equation and get a=3
then you make the a percentage which is 300%
you subtract 100% because that is what you began with and get 200%
The fraction will change by 200%.
Let the fraction is = x/y.
If its numerator is decreased by 10% then the new numerator is:
x - 10% of x
= x - 0.10x
= 0.90x
If its denominator is decreased by 70% then the new denominator is:
y - 70% of y
= y - 0.70y
= 0.30y
So the new fraction is = [tex]\frac{0.90x}{0.30y}=\frac{3x}{y}[/tex].
So the change in fraction is in percentage is:
[tex]\frac{\left(new\ -old\right)}{old}\cdot100\\=\frac{\left(\frac{3x}{y}-\frac{x}{y}\right)}{\frac{x}{y}}\cdot100\\=\frac{\left(\frac{2x}{y}\right)}{\frac{x}{y}}\cdot100\\=200[/tex]
So the fraction will change by 200%.
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