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Linear Inequalities in One or Two Variables

SAT Math· difficulty 4/5

A worker earns \15/hregularand/h regular and $22/hovertime(over40h).Toearnatleast/h overtime (over 40 h). To earn at least $700inaweek,howmanyovertimehoursin a week, how many overtime hoursx$ are needed?

  • A

    x≥5x \ge 5

  • B

    x≥6x \ge 6

  • C

    x≥10022x \ge \frac{100}{22}

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  • D

    x≥10x \ge 10

Explanation

15(40)+22x≥700⇒600+22x≥700⇒x≥100/22≈4.5515(40) + 22x \ge 700 \Rightarrow 600 + 22x \ge 700 \Rightarrow x \ge 100/22 \approx 4.55.

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