Problem Solving

Hi VJesus12,

We're told that a soda machine sells both bottles and cans, and no other items. Bottles cost $1.50 each, while cans cost $0.75 each and in one day, the soda machine sold 250 total beverages and yielded $315. We're asked how many MORE bottles than cans were sold. This question can be approached in a number of different ways; here's how you can use a 'comparison' to get to the correct answer.

While we know that some bottles and some cans were sold, IF all 250 items sold were bottles, then THAT revenue would be (250)($1.50) = (125)($3) = $375.

For each bottle that we 'trade' for a can, we 'lose' $0.75 from the total revenue. To get $375 down to $315, we have to 'lose' $60 (in $0.75 increments). That would be...
60/.75 =
120/1.5 =
240/3 =
80 cans

With 250 items sold, there would be 80 cans and 170 bottles - and that would be 170 - 80 = 90 MORE bottles than cans.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

VJesus12 wrote:A soda machine sells both bottles and cans, and no other items. Bottles cost $1.50 each, while cans cost $0.75 each. If on one day, the soda machine sold 250 total beverages and yielded $315, how many more bottles than cans were sold?

A) 60
B) 80
C) 90
D) 115
E) 170

We can let b = the number of bottles of soda sold and c = the number of cans of soda sold, and create the equations:


b + c = 250

and

1.5b + 0.75c = 315

Multiplying the first equation by 3, we have 3b + 3c = 750.......[Eq. 1]

Multiplying the second equation by 4, we have 6b + 3c = 1260...... [Eq. 2]

Subtracting Eq. 1 from Eq. 2, we have 3b = 510. So b = 510/3 = 170.

Since b + c = 250, so c = 250 - 170 = 80.

Therefore, the number of bottles sold is 170 - 80 = 90 more than the number of cans sold.

Answer: C