Hi -
Might as well throw my $0.02 in.
I'm not sure which way you are trying to work this problem, so I will work it both ways:
0.33x = 11
Which means X is 33.33 as everyone agrees. But to maintain balance to the equation, you have to multiply both sides by 1.1 (or a 10% increase) which gives you:
1.1 * 0.33x = 11 * 1.1
or
0.363x = 12.1 which still equates to x = 33.33 so our formula is still valid and balanced.
I think the problem is SAYING 10% takes you from 33% to 43%, which isn't true. You can't add the two percentages. You have to multiply. So you should end up with 36.3%, not 43%.
Working the problem the other way: IF you WANT the result to BE 43% of the original number, you would have to multiply 11 by 1.3029. I get that by taking 33.33 x 0.43 = 14.3319
14.3319 / 11 = 1.3029 which is an increase of 30.29%, not 10%.
Taking percentages of percentages can get really tricky. I have to write them out as I did above.
Make sense or am I way off base?
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