Question 130917: a newsagent buys 100 overseas magazines and pays $100 for them. He buys American magazines for $10, British for $5 and comics for 50 cents each how many of each does he buy?
thank you so much really appreciate your help
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=number of American
Let y=number of British
Let z=number of comics
Now we know that
10x+5y+0.5z=100-----------------eq 1
we also know that:
x+y+z=100-----------------------eq 2
Two equations in three unknowns means that we need to do some smart guessing.
First, multiply eq1 by 2 and then subtract eq2 from it.
20x+10y+z=200 minus x+y+z=100 equals:
19x+9y=100 subtract 9y from each side
19x=100-9y divide each side by 19
x=((100-9y)/19)---------------EQ3
Now we have a relation between the number of American magazines and the number of British magazines and here is where we do some smart figuring:
First, we cannot have a fraction of a magazine (our answers have to be whole numbers)
And secondly, we cannot have negative magazines.
Armed with this information, lets take a look at EQ3
We can see that y cannot be greater than 11 lest we have negative American magazines. So lets set up a table and see what we have
If y=1; x=91/19-----------------NO GOOD ---FRACTION OF MAG
If y=2; x=82/19-------------------NO GOOD----FRACTION OF MAG
If y=3; x=73/19---------------------NO GOOD---FRACTION OF MAG
If y=4; x=64/19------------------------NO GOOD----FRACTION OF MAG
If y=5; x=55/19----------------------NO GOOD---FRACTION OF MAG
If y=6; x=46/19-----------------------NO GOOD----FRACTION OF MAG
If y=7; x=37/19-------------------------NO GOOD---------FRACTION OF MAG
If y=8; x=28/19--------------------------NO GOOD--FRACTION OF MAG
If y=9; x=19/19=1---------------------BINGO!!!!!
If y=10; x=10/19----------------------------------NO GOOD---FRACTION OF MAG
If y=11; x=1/19------------------------------NO GOOD---FRACTION OF MAG
So our only possibilities are:
x= # of American Magazines=1
y=# British Magazines=9
Then z=# of comics would have to equal=90
CK
1+9+90=100
100=100
9*5+1*10+90*0.5=100
100=100
Hope this helps---ptaylor
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