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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?
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
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?
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
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portion of pie
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?
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=75 windows total
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?
x+y=10(3z)
x+y=30z
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?
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
Hope this helps,
Prabhat
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