# arithmetic problem

• Apr 13th 2010, 08:45 AM
sri340
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
• Apr 13th 2010, 10:49 AM
fizzle45
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
\$\displaystyle \\$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)
\$\displaystyle 1x+1y=24\$

now we solve using these 2 equations.

\$\displaystyle 1x+3y=28\$
\$\displaystyle 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)