Question 962182: Hi, I have been trying to solve this question but it proves to be a hard nut to crack. Can you please help me out? The question is thus;
Alex lives with his parents. All of them have a job. Once
they calculated that if Alex earned twice as much, the
total income of their family would have increased by 5%.
Instead, if his mother’s earning increased by 50%, the
total family income would have increased by 20%. By
what percent would the family total income increase if
only the father’s earnings have increased by 20%?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! let a = Alex's income
let m = Mom's income
let f = Dad's income
then
t = total original income (a+m+f)
:
they calculated that if Alex earned twice as much, the total income of their family would have increased by 5%.
a + t = 1.05t
a = 1.05t - t
a = .05t is A's salary
:
Instead, if his mother’s earning increased by 50%, the total family income would have increased by 20%.
.5m + t = 1.2t
.5m = 1.2t - t
.5m = .2t
multiply by 2
m = .4t is Mom's salary
:
We know that a + m + f = t
t = .05t + .4t + f
f = t - .45t
f = .55t is Dad's salary
:
"By what percent would the family total income increase if only the father’s earnings have increased by 20%?"
1.2 * .55t = .66t, Dad's increased salary
therefore: .66t - .55t = .11t. A 11% increase in total income
:
:
See if we can check this; assume the family income is $1000
then
.05 * 1000 = $50 a month is Alex's salary
.40 * 1000 = $400 a month is Mom's salary
.55 * 1000 = $550 a month is Dad's salary
Dad's salary is increase by 20%: 1.2 * 550 = $660 a months, $110 more
110/1000 * 100 = 11% increase
:
:
Seems like there should be an easier way to do this, but I cannot come with it.
CK, ankor@att.net
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