ACT Math · Function notation and transformations

A shipping company charges 5 for packages weighing 2 pounds or less, and 5 plus $1.50 per pound over 2 pounds for heavier packages. What…

A shipping company charges $5 for packages weighing 2 pounds or less, and $5 plus $1.50 per pound over 2 pounds for heavier packages. What is the cost to ship a 5-pound package?

Answer and explanation

Answer: D: $9.50

The package weighs 55 pounds, which is more than 22 pounds, so use the second rule: $5 plus $1.50 for each pound over 22. The excess is 5−2=35-2=3 pounds, so the cost is 5+1.50(3)=5+4.50=9.505+1.50(3)=5+4.50=9.50 dollars, choice D. Choice B ($12.50) applies the $1.50 rate to all 55 pounds, 5+1.50(5)5+1.50(5), instead of just the excess. Choice A ($7.50) is 1.50⋅51.50\cdot5 with no base fee. Choice C ($11.00) comes from charging for 44 extra pounds. Piecewise cost rules charge the per-pound rate only on the part above the threshold.

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