Question 1177738: Mr Lim will pay $ y to Michael and $80 less than Michael to Jack monthly for x months. The total amount will be received by Michael in x months is $2400.
In the next coming x months, each of them are given $20 more than the money they receive in the previous x months monthly. Given that the total amount will be received by both of them together in the next x months is increased by 12.5% compared to the total amount will be received by both of them in the previous x months. Calculate the values of x and y.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! y = the amount that michael is paid each month for x months.
y-80 = the amount that jack is paid each month for x months.
y*x = the total amount that michael is paid in x months.
since the amount that michael is paid in x months is 2400, you get:
y*x = 2400
that's for the first x months.
in the next x months, each of them is paid 20 dollars more each month and the total amount they both get paid is 12.5% more than they got paid for the previous x months.
this means that michael gets paid (y+20)*x and jack gets paid (y-80+20) = (y-60)*x for the next 12 months.
you get:
(y+20)*x + (y-60)*x = (y*x + (y-80)*x)) * 1.125
simplify this to get:
y*x + 20*x + y*x - 60*x = y*x*1.125 + (y-80)*x*1.125
simplify further to get:
2*y*x - 40*x = y*x*1.125 + y*x*1.125 - 80*x*1.125
combine like terms to get:
2*y*x - 40*x = 2*y*x*`1.125 - 80*x*1.125
subtract 2*y*x from both sides of the equation and add 80*x*1.125 to both sides of the equation to get:
80*x*1.125 - 40*x = 2*y*x*1.125 - 2*y*x
factor out x on the left side of the equation and y*x on the right side of the equation to get:
x*(1.125*80 - 40) = y*x*(2*1.125 - 2*1)
combine like terms and simplify to get:
50*x = .25*y*x
you had previously calculated that y*x = 2400, so replace y*x with 2400 to get:
50*x = .25*2400 = 600
solve for x to get:
x = 600 / 50 = 12.
the number of months is 12.
since y * x = 2400, then solve for y to get:
y = 2400/12 = 200
this makes y-80 equal to 120.
michael gets 200 each month and jack gets 120 each momnth for the first 12 months.
the total they get for the first 12 months is 12*200 + 12*120 = 12*(320) = 3840.
the total they get for the next 12 months is 12*220 + 12*140 = 12*(360) = 4320.
4320/3840 = 1.125.
everything looks good.
your answer is that x = 12 and y = 200.
|
|
|
