Question 1163252: Manny spends 8% salary on council tax. Gloria pays the same amount of council tax as Manny but this only represents 5% of her salary. How much does
Gloria earn?
Thanks :)
Found 2 solutions by jim_thompson5910, Theo:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
M = Manny's salary
G = Gloria's salary
8% of M = 0.08M = amount Manny pays in tax
5% of G = 0.05G = amount Gloria pays in tax
We set 0.08M and 0.05G equal to each other since Gloria pays the same amount of tax as Manny does.
0.08M = 0.05G
8M = 5G
8M/5 = G
G = 8M/5
G = (8/5)M
G = 1.6M
We don't have enough information to solve any further. We need more information to be able to set up another equation to solve for M and G. At this point, we're stuck. We do know that Gloria's salary is 1.6 times that of Manny's salary.
I would ask your teacher for clarification.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! since you don't know how much either of them made, you can't answer this question.
you can, however, determine how much more gloria made than manny.
let M be the amount of money that manny made.
manny's tax was therefore .08 * M.
let G be the amount of money that gloria made.
gloria's tax is therefore .05 * G.
since the amount of tax that gloria paid was the same as the amount of tax that manny made, you get:
05 * G = .08 * M
solve for G to get:
G = .08 * M / .05 = 1.6 * M.
this says that gloria made 1.6 times as much as manny made.
that's as far as you can go unless you know what either manny made or gloria made.
assuming you know that manny made 100,000 dollars.
this means that gloria made 160,000 dollars.
.08 * 100,000 = 8,000
.05 * 160,000 = 8,000
they paid the same tax if gloria made 1.6 times as much as manny.
assuming you know that gloria made 160,000
since G = 1.6 * M, then M = G / 1.6.
this means manny made 160,000 / 1.6 = 100,000 dollars.
you get the same solution.
without knowing what either of them made, you can only know that gloria has to made 1.6 times as much as manny makes, whatever that is.
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