Multiple choice

Four grades of oil are 2%, 5%, 8%, and 11% additive by volume. If p liters of the 2% grade, q liters of the 5% grade, r liters of the 8% grade, and t liters of the 11% grade are mixed to form p + q + r + t liters of a mixture that is 6% additive by volume, then what is p in terms of q, r, and t?

  1. − q + 2 r + 5 t 4

  2. − q + 2 r − 5 t 4

  3. q − 2 r − 5 t 6

  4. q − 2 r + 5 t 6

  5. − q − 2 r + 5 t 6
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A Correct answer
Explanation

0.02p + 0.05q + 0.08r + 0.11t = 0.06(p + q + r + t). Multiply by 100: 2p + 5q + 8r + 11t = 6p + 6q + 6r + 6t. Rearrange: 4p = -q + 2r + 5t. p = (-q + 2r + 5t) / 4.

AI explanation

Setting up the weighted average equation gives 0.02p + 0.05q + 0.08r + 0.11t = 0.06(p + q + r + t). This simplifies to 2p + 5q + 8r + 11t = 6p + 6q + 6r + 6t, meaning 4p = -q + 2r + 5t. Therefore, p equals (-q + 2r + 5t) / 4.

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