Problem Solving

BTGmoderatorLU wrote:Java House charges $3.25 for a cup of coffee that costs a total of $2.85 to make. Cup'O'Joe charges $2.80 for a cup that costs $2.65 to make. If Java House sells 55,000 cups of coffee, how many must Cup'O'Joe sell to make at least as much in total gross profit as its competitor does?

A. 7,858
B. 8,301
C. 14,667
D. 63,840
E. 146,667

The OA is E.

I solve this PS question as follows,

Gross profit made by Java House = (3.25 - 2.85)*55,000

Gross profit made by Cup'O'Joe = (2.80 - 2.65)*X, where X is the number of cups Cup'O'Joe needs to sell.

In order for Cup O Joe of break even with Java House equate the two equations

( 3.25 - 2.85 ) * 55000 = (2.80 - 2.65 ) * X

X = (0.4 * 55000 ) / 0.15
= 146,666.4 .

Hence, E is the correct answer.

Please, can anyone explain another way to solve this question? Thanks in advance!

This is all fine.

-Jay
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Hi All,

We're told that Java House charges $3.25 for a cup of coffee that costs a total of $2.85 to make, Cup'O'Joe charges $2.80 for a cup that costs $2.65 to make and Java House sells 55,000 cups of coffee. We're asked for the number of cups that Cup'O'Joe must sell to make at least as much in total gross profit as its competitor does. The 'math' behind this question can be done in a number of different ways, but we can use the 'spread' of the answer choices to our advantage and avoid doing lots of math.

Based on the given information...
Java House makes a profit of $3.25 - $2.85 = $0.40 per cup of coffee sold.
Cup 'O' Joe makes a profit of $2.80 - $2.65 = $0.15 per cup of coffee sold.

Notice how Java house makes MORE than TWICE the profit per cup sold as Cup 'O' Joe makes. Thus, for Cup 'O' Joe to make as much total profit as Java House makes, it will have to sell MORE than DOUBLE the number of cups that Java House sells. Based on the data, Java House sells 55,000 cups, so Cup 'O' Joe will have to sell well more than 110,000 cups. There's only one answer that fits.

Final Answer: E

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

BTGmoderatorLU wrote:Java House charges $3.25 for a cup of coffee that costs a total of $2.85 to make. Cup'O'Joe charges $2.80 for a cup that costs $2.65 to make. If Java House sells 55,000 cups of coffee, how many must Cup'O'Joe sell to make at least as much in total gross profit as its competitor does?

A. 7,858
B. 8,301
C. 14,667
D. 63,840
E. 146,667

The profit per cup for Java House is 3.25 - 2.85 = $0.40.

So they make a total of 55,000 x 0.4 = $22,000 gross profit.

The profit per cup for Cup'O'Joe is 2.80 - 2.65 = $0.15.

So they must sell a total of 22,000/0.15 = 146,667 cups of coffee.

Answer: E