Armed Forces Classification Test (AFCT) Arithmetic Reasoning Practice Test

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Study for the AFCT Arithmetic Reasoning Test. Explore in-depth questions, enhance problem-solving skills with hints and detailed explanations. Ace your assessment!

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You send 700 pounds of fruit; some boxed and some unboxed. If the boxed fruit costs $0.07 per pound to mail and the unboxed fruit costs $0.06 per pound to mail, how many pounds of boxed fruit did you send if the bill for mailing the fruit was $45.00?

300 pounds
400 pounds
500 pounds
200 pounds

The correct answer is: 300 pounds

To determine the correct amount of boxed fruit sent, start by defining two variables: let $ x $ represent the weight of the boxed fruit in pounds, and subsequently, the weight of the unboxed fruit can be expressed as $ 700 - x $ because the total weight is 700 pounds. Next, calculate the mailing costs based on the cost per pound for both boxed and unboxed fruit. The cost to mail the boxed fruit is $ 0.07x $, and the cost to mail the unboxed fruit is $ 0.06(700 - x) $. The total mailing cost is given as $45. Therefore, we can set up the following equation that combines the costs: \[ 0.07x + 0.06(700 - x) = 45 \] Now, simplify the equation: 1. Distributing $ 0.06 $ in the second term results in $ 0.06 \times 700 = 42 $ and $ -0.06x $. 2. Combine like terms: \[ 0.07x - 0.06x + 42 = 45 \] This simplifies to: \[ 0.01x +