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Math Help - arithmetic problem

  1. #1
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    arithmetic problem

    A store sells juice in two sizes of bottles: small and large. A large bottle costs three times as much as a small one . jack bought 10 small bottles and 6 large bottles . with the same amount of money , Lise bought 24 bottles . how many little bottles did Lise buy ?

    A 16 b 18 c 20 d 22 e not enough information
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  2. #2
    Junior Member
    Joined
    Aug 2009
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    its D 22 bottles
    basically i just assumed small bottles were 1 dollar and large were 3 dollars then found the budget the first dude that bought 16 bottles $(1 x 10 + 3 x 6)= $28. and used that same budget to determine the girls amount of small bottles using her limit of 24 bottles as a constraint.


    ok for the way with equations. this problem can be expressed as 2 equations with 2 unknown varibles. then we can use our algebra to solve

    first equation (still using the price of bottles as 1$ for small 3$ for large)
    since we know bill or dave or watever spent 28 dollars on his bottles we can express that as
    \$1x+\$3y=\$28
    here i am using x as the small bottles and y as the big bottles.

    now for the second equation since we know that lisa has to buy 24 bottles (a mix of small (x) and large (y) bottles)
    1x+1y=24

    now we solve using these 2 equations.

    1x+3y=28
    1x+1y=24

    if we multiply the bottom equation by (-1) and then add the 2 equations we are able to solve for y. once you obtain this value for y you can plug that value into either of the 2 equations to obtain x (which is the amount of small bottles lisa bought, and your answer)
    Last edited by fizzle45; April 13th 2010 at 12:00 PM.
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