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sum of the ages

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by sairakesh » Wed Jul 01, 2009 5:26 am
The sum of the ages of 22 boys and 24 girls is 160.What is the sum of ages of one boy plus one girl, if all the boys are of the same age and all the girls are of the same age, and only full years are counted?
1.6
2.7
3.5
4.8
5.9
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by truplayer256 » Wed Jul 01, 2009 6:40 am
This is more of a guess and check question.

X= Age of one boy
Y= Age of one girl

22X+24Y=160

We want X+Y=?

Just to make the numbers more simpler and easier to work with, let's factor out a 2.

2(11X+12Y)=160

11X+12Y=80

X=4--> 12Y=36--> Y=3

X+Y=4+3=7 B
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by shanmugam.d » Wed Jul 01, 2009 8:15 am
to continue with trueplayer:
11X+12Y=80 to find the combination which makes up 80
just list multiples of 11: 11 22 33 44 55
multiple of 12: 12 24 36 48 56
the combination is: 4 & 3 hence: 4+3 = 7 (B)
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maybe if we find x first?

by ajlcalbanese1 » Wed Jul 01, 2009 8:51 am
if we have:
22X+24Y=160

can we find the value for X and then substitute in the ecuation?

22x=160-24y

x=160-24y/22

22(160-24y/22)=160

and from here find the value of y and substitute in the ecuation?

would that work? any comments about my aproach?
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by scoobydooby » Wed Jul 01, 2009 11:22 am
22B+24G=160
=>11B+12G=80

80 is even, 12G is even=> 11B must be even (E+E=E)
since B, G must be integers,
G=(80-11B)/12 must be an integer

let B be 2, (B must be even)=>G=(80-22)/12=58/12 not an integer
let B be 4, (G=80-44)/12=36/12=3 integer. bingo!

so B+G=4+3=7

hence, B
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thanks

by sairakesh » Thu Jul 02, 2009 5:37 am
thanks a lot for ur help.
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by ghacker » Thu Jul 02, 2009 8:31 am
Another way

Girls = G ; Boys = B

22B+24G = 160 , B, G integers
22(B+G) +2G = 160 -------------> 11(B+G)+G = 80

Since B, G are integers B+G must also be an integers and the only positive integers which satisfy the equations are 7 and 3

So G = 3 and B= 4
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