Question 18555
hi! kindly provide me solutions for this problem, thanks a lot!
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1) There is a large cookie jar filled with 45 cookies.  If the cookies are distributed in a 2:3:4 ratio among three children, what is the greatest number of cookies that any one child receives?
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Let the ratio be in terms of x
2x+3x+4x=45
9x=45
x=5
greatest number of cookies=4x=4(5)=20 to the third child
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2) Two boys and one girl evenly split one apple pie.  If one boy gives ½ of his piece to the girl and the other boy gives ¾ of his piece to the girl, what fraction of the entire pie does the girl now have?
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Let the pie be x
Then they evenly split the pie
hence 2 boys and 1 girl,each gets: (x/3)
one boy gives the girl 1/2 his portion: (x/3-1/2)=[(2x-3)/6]
the other gives 3/4th : (x/3-3/4)=[(4x-12)/12]
Now the girl has: (x/3)+both of the other portions
={{{(x/3)+((2x-3)/6)+((4x-12)/12)}}}
={{{(4x+2(2x-3)+(4x-12))/12}}}
={{{(4x+4x-6+4x-12)/12}}}
={{{(12x-18)/12}}}
={{{6(2x-3)/(6*2)}}}
={{{(2x-3)/2}}} portion of pie
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3) 30 of a building’s windows have shades.  If 2 of every 5 windows are shaded, then how many windows does the building have?
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let the number of windows be x
out of x,30 have shades
now,out of 5,2 windows have shade
x:30=5:2
{{{x/5=30/2}}}
{{{x=(30/2)*5}}}
x=75 windows total
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4) The sum of x and y is 10 times more than 3 times z.  Which of the following equations describes the relationship between x, y, and z?
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x+y=10(3z)
x+y=30z
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5)A gas pump pumps x liters of gas every y minutes.  If gas costs Pz a liter, and the pump automatically stops after dispensing gas for m minutes, how much does the dispensed gas cost?
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Rate of pumping gas=No.of liters/No. of minutes
=x liters per y minutes
=(x/y)l/min
Number of minutes pumped=m
Therefore,number of ltrs dispensed=(x/y)*m
Cost of one ltr=Pz
Hence cost of dispensed litrs=Pz*(x/y)*m
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Hope this helps,
Prabhat