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A soda machine sells both bottles and cans, and no other

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A soda machine sells both bottles and cans, and no other

by VJesus12 » Mon May 28, 2018 2:10 am

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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

The OA is the option C .

What is the best approach for solving this PS question? Could someone give me an explanation here? Thanks.
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by GMATGuruNY » Mon May 28, 2018 2:33 am
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
Price per bottle = 150 cents.
Price per can = 75 cents.
Average price for the MIXTURE of bottles and cans = (total revenue)/(total number of beverages) = (315 dollars)/(250 beverages) = 63/50 dollars = 126/100 dollars = 126 cents.

To determine the ratio of bottles to cans, we can use ALLIGATION.

Step 1: Plot the 3 prices on a number line, with the prices for bottles and canes on the ends and the price for the mixture in the middle.
B 150---------------------126----------------------75 C

Step 2: Calculate the distances between the averages.
B 150---------51---------126---------24---------75 C

Step 3: Determine the ratio in the mixture.
The ratio of bottles to cans is equal to the RECIPROCAL of the distances in red.
B:C = 24:51 = 8:17 = 80:170.

The ratio in blue implies that B=80 and C=170, for a total of 250 beverages.
Thus:
C-B = 170-80 = 90.

The correct answer is C.
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by Brent@GMATPrepNow » Mon May 28, 2018 5:05 am
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
Let B = # of bottles sold
Let C = # of cans sold

If on one day, the soda machine sold 250 total beverages...
We can write: B + C = 250

...and yielded $315.
So: 1.5B + 0.75C = 315
We can eliminate the decimals by multiplying both sides by 4 to get: 6B + 3C = 1260

How many more bottles than cans were sold?
So, we must determine the value of B - C.

We have the system:
B + C = 250
6B + 3C = 1260

When we solve this system for B and C , we get: B = 170 and C = 80
So, B - C = 170 - 80 = 90

Answer: C

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by [email protected] » Mon May 28, 2018 11:34 am
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

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by Jeff@TargetTestPrep » Wed May 30, 2018 4:20 pm
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

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Head of GMAT Instruction
[email protected]

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