Question 1201236: Before Marium changed jobs, her salary was 24 percent more than Maria’s salary. After Marium changed jobs, her new salary was 24 percent less than her old salary. If quantity A is Maria’s salary and quantity B is Marium’s new salary, then:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! A = maria's salary
B = marium's salary
before changing jobs, marium's salary was 24% more than maria's.
equation for that is B = 1.24A
after changing jobs, marium's salary wwas 24% less than her previous salary.
equation for that is:
B = .76B
since B = 1.24A in the first equation, then replace B with 1.24A in the right side of the second equationA to get:
B = .76 * 1.24A
simplify to get:
B = .9424A.
this suggests that, before she changed jobs, her salary was 24% higher than marium's, and after she changed jobs, her salary was 94.24% as large as mariuum's.
94.24% as large means that it is 5.76% less than marium's (94.24% minus 100% =
-(100 = 94.24) = -5.76%.
to see if this makes sense, then pick a salary for maria, at random, that makes some kind of sense, like 20,000 per year.
since marium's salary, before she changed jobs, was 24% higher, then marium must have been making 24,800.
when marium changed jobs, she would have been making .76 * 24,800 = 18,848.
20,000 minus 18,848 = 1,152
1,152 / 20,000 = .0576.
.0576 * 100, = 5.76%.
marium was now making 1,152 less than 20,000 which is 5.76% less than 20,000
18,848 is also 18,848 / 20,000 = .9424 as large as 20,000.
multiply that by 100, which makes it 94.24% as large as 20,000.
the figures check out, so the solution looks good.
i'm not exactly sure what you are looking for, but i get:
marium's new salary is 94.24% as large as maria's, which is 5.76% less than maria's.
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