Problem Solving

Princeton Review

A magazine stand owner sells cups of coffee, newspapers, and packs of gum. Compared to the number of cups of coffee he sells, he sells twice as many packs of gum, and three times as many newspapers. If he charges $1.25 for a cup of coffee, $.50 for a newspaper, and $.35 for a pack of gum, and sells no other items, which of the following could be the amount of his total gross sales on a given day?

I.$345.00
II.$58.65
III.$22.15

A. I only
B. I + II only
C. I + III only
D. II and III only
E. I, II and III only

OA B

Let the number of coffee cups sold = c
Let the number of the newspaper sold = n
Let the number of gums sold = g

Compared to cups of coffee, he sells twice as many packs of gum and three times as many newspapers
g = 2c and n = 3c

Price of c = $1.25
Price of n = $0.50
Price of g = $0.35

Total gross sales = (1.25 * c) + (0.50 * n) + (0.35 * g)
=1.25c + 0.50n + 0.35g where n = 3c and g = 2c
Therefore, total gross sales = 1.25c + (0.50 * 3c) + (0.35 * 2c)
=1.25c + 1.5c + 0.7c
=3.45c

Total sales for any given day = $3.45 * c; where c = quantity of cups of coffee which must be a positive integer

Target question => Which of the following could be the amount of his total gross sales on a given day?

For $345.00 =>
3.45c/3.45 = 345/3.45
c = 100, c is a positive integer so gross sales could be $345.00

For $58.65 =>
3.45c = 58.65 and c = 17
c is a positive integer, gross sales could be $58.65

For $22.15 =>
3.45c = 22.15 and c = 6.42
It is not possible to sell a fraction of a cup of coffee. c is positive but not an integer so gross sales cannot be $22.15

Only option I and II is possible
Answer = B