SAT Systems of two linear equations in two variables Practice Question 20 (Hard)

Question bank / Systems of two linear equations in two variables

Math · AlgebraHard

A store ships candles in small boxes that hold $6$ candles each and large boxes that hold $15$ candles each. One shipment contained $40$ boxes, all filled, holding a total of $393$ candles. How many small boxes were in the shipment?

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Answer: 23

Let $s$ be small boxes and $l$ large boxes: $s + l = 40$ and $6s + 15l = 393$ . Substitute $s = 40 - l$ : $240 - 6l + 15l = 393$ , so $9l = 153$ and $l = 17$ . Then $s = 40 - 17 = 23$ .

Giving 17 answers with the number of large boxes instead of small boxes.

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