Louis works two days a week: 8 hours every Saturday and 6 ho

Question

Louis works two days a week: 8 hours every Saturday and 6 hours every Sunday. He earns twice as much per hour on Sunday as he does on Saturday. If in a certain month, he earned $720 from the hours he worked on Saturdays and $1,350 from the hours he worked on Sundays, how much did he earn during the following month?

(A) $1,620
(B) $1,800
(C) $1,890
(D) $1,980
(E) $2,070

(A) $1,620
(B) $1,800
(C) $1,890
(D) $1,980
(E) $2,070

modiassumenda · Answer

Let Saturday hourly wage = S.
Then Sunday hourly wage = 2S.
From the first month:
Saturday earnings = $720
He works 8 hours each Saturday, so:
8 × (number of Saturdays) × S = 720
Sunday earnings = $1350
He works 6 hours each Sunday, so:
6 × (number of Sundays) × 2S = 1350
12 × (number of Sundays) × S = 1350
Divide the two equations:
720 / 1350 =   /  
16 / 30 = 2(Saturdays) / 3(Sundays)
48(Sundays) = 90(Saturdays)
8(Sundays) = 15(Saturdays)
The only possible month with 4 or 5 weekends satisfying this is:
Saturdays = 4 and Sundays = 5
Now find S:
8 × 4 × S = 720
32S = 720
S = 22.5
So:
Saturday wage = $22.50/hour
Sunday wage = $45/hour
The following month must have:
5 Saturdays and 4 Sundays
Saturday earnings:
5 × 8 × 22.5 = 900
Sunday earnings:
4 × 6 × 45 = 1080
Total earnings:
900 + 1080 = 1980
Answer:  D  ( $1,980 )

shashank35 · Answer

for saturday the H= 8 , R=x, N=? = we need to mutiply something with 8x to get 720 FOR SUNDAY , H=6, R=2x, = 1350 so we need to multiply something with 12x to get 1350. 8x/12x = 2:3 720/1350 the ratio is smaller than 2:3 so we can say sundays need to be greater than saturdays i.e 4,5 fpr this month. checking for this 8x *4 = 720 x=22.5 , 12x*5= 1350 , X =22.5 so we werre corect in asuming. in following month saturdays and sundays eah will be 4 only. when sat came 4 times it should remain same i.e 720 for sunday 4 times it will be 1350/5*4 = 1080. 1080+720 = 1800 b) ANS

chetan2u · Answer

Every month will surely have four of each days and depending on the month, there will be five of few. 
 Saturday's earning :  8*x
 Sunday's earning :  6*2x or 12x
Thus he earns 12x/8x or 1.5 times on Sundays.
If there were equal numbers of Satudays and Sundays, earning on Sundays would be 720*1.5, that is 1080. But that is not the case.
 Since earning on Sundays is more than 1080, we are lookong at more Sundays. Thus  4 Saturdays and 5 Sundays, which further means the month started with Sunday.  
   The next month will never have five of the day the previous month started or the previous day to that day..  
 If month starts on Sunday, it will end on Sunday(29 days month), or on Monday(30 days month) or on Tuesday(31 days).Even if the both month have 31 days, that is it starts on Wednesday, it will end on Friday. This means we will have four of each of Sat and Sun. 
 The total = 4(8x+12x) = 720+720*1.5 = 720(1+1.5) = 720*2.5 = 720*5/2 = 360*5 = $1800

D

Louis works two days a week: 8 hours every Saturday and 6 ho

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