You are given a mathematical question described with an open-ended vocabulary. Questions in this task involve real-world situations, describing a mathematical problem. You are also given 4 or 5 answer options (associated with "A", "B", "C", "D", "E"). Do not generate anything else apart from one of the following characters: 'A', 'B, 'C', 'D', 'E'. LaTeX mathematical format (the standard way to express mathematical expressions in the typesetting software known as LaTeX) is used to express equations. Each question is solvable with high school math knowledge. Give only one answer for each question.
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Question: The force needed to stretch a spring varies directly with the distance the spring is stretched from its equilibrium position. If 50 pounds of force stretch a spring 8 inches from equilibrium, how much, in inches, will the spring be stretched by a force of 75 pounds?
(A)10 (B)12 (C)33 (D)248 (E)468.75

Answer: B


Question: David has 4 less than one-half the number of balloons that Katie has. If David has d balloons, and Katie has k balloons, which of the following equations correctly expresses the relationship between \(d\) and \(k\) ?
(A)\(d = \frac { 1 } { 2 } (k + 4)\) (B)\(d = \frac { 1 } { 2 } (k - 4)\) (C)\(d = \frac { 1 } { 2 } k + 4\) (D)\(d = \frac { 1 } { 2 } k - 4\) (E)\(d = 2 (k - 4)\)

Answer: D


Question: If a mixture of nuts consists of 3 pounds of peanuts, I pound of walnuts, and 5 pounds of cashews, by weight, what fraction of the mixture is peanuts?
(A)\(\frac { 1 } { 9 } \) (B)\(\frac { 1 } { 5 } \) (C)\(\frac { 1 } { 3 } \) (D)\(\frac { 3 } { 8 } \) (E)\(\frac { 1 } { 2 } \)

Answer:
C