ExpertsGlobal5
Arnold purchased 10 pounds of caramel, 5 pounds of nougat, and 6 pounds of marshmallows from a wholesale confectionary for a total of $43. If the price for each confection is directly proportional to its weight, what is the price of 1 pound of caramel and 3 pounds of marshmallows?
(1) Phillip purchased 4 pounds of caramel and 4 pounds of nougat for a total of $14.
(2) Mary purchased 8 pounds of caramel and 5 pounds of nougat for a total of $22.
Explanation: Amount of caramel purchased = 10 pounds.
Amount of nougat purchased = 5 pounds.
Amount of marshmallows purchased = 6 pounds.
Since the price for each confection is directly proportional to its weight:
Price of 10 pounds of caramel = 10C, where C is the constant of proportionality.
Price of 5 pounds of nougat = 5N, where N is the constant of proportionality.
Price of 6 pounds of marshmallow = 6M, where M is the constant of proportionality.
Since the total price is given as $43: 10C + 5N + 6M = 43 (Equation I)
Price of 1 pound of caramel and 3 pounds of marshmallow = 1C + 3M = C + 3M
We need to find whether the value of C + 3M can be determined. Statement (1) 4C + 4N = 14 (Equation II)
Substituting Equation II into Equation I does NOT help us determine the value of C + 3M.
Hence, Statement (1) is insufficient. Statement (2) 8C + 5N = 22
5N = 22 – 8C
Substituting the value of 5N into Equation I:
10C + 5N + 6M = 43
10C + 22 – 8C + 6M = 43
2C + 22 + 6M = 43
2C + 6M = 21
Dividing both sides by 2, we get:
C + 3M = 10.5
It is possible to determine the value of C + 3M.
Hence, Statement (2) is sufficient. B is the correct answer choice.