Question

patties produce charges $2.29 for a package of strawberries. on average, patties produce sells 95 packages of strawberries daily. they estimate that for each 20 - cent increase in the cost of a package of strawberries, 9 fewer packages will be sold each day. let x represent the number of 20 - cent increases in the cost of a package of strawberries. which inequality represents the values of x that would allow patties produce to have a daily revenue of at least $255 from selling the packages of strawberries? a. $-1.8x^{2}+1.61x + 217.55leq255$ b. $-1.8x^{2}-21.61x + 217.55leq255$ c. $-1.8x^{2}-1.61x + 217.55geq255$ d. $-1.8x^{2}+21.61x + 217.55geq255$

Explanation:

Step1: Define price per package

Price = $2.29 + 0.20x$

Step2: Define number of packages sold

Quantity = $95 - 9x$

Step3: Calculate revenue

Revenue = Price × Quantity = $(2.29 + 0.20x)(95 - 9x)$

Step4: Expand the revenue expression

$(2.29)(95) + (2.29)(-9x) + (0.20x)(95) + (0.20x)(-9x) = 217.55 - 20.61x + 19x - 1.8x^2 = -1.8x^2 -1.61x +217.55$ (correction: $-20.61x +19x = -1.61x$ → error in earlier sign, but target is "at least 255" so ≥ 255. Wait, recheck: $2.29×(-9)= -20.61$, $0.2×95=19$, so $-20.61x +19x = -1.61x$. But option D has +21.61x? Wait no—wait 9 fewer per 20-cent increase: yes, quantity=95-9x. Price=2.29+0.2x. Revenue=(2.29+0.2x)(95-9x)=2.29×95 +2.29×(-9x)+0.2x×95 +0.2x×(-9x)=217.55 -20.61x +19x -1.8x²= -1.8x² -1.61x +217.55. "At least 255" means revenue ≥255, so $-1.8x² -1.61x +217.55 ≥255$ → but option C is this. Wait wait—wait did I mix up increase/decrease? No, problem says 9 fewer per 20-cent increase. Wait option C is exactly this. Oh yes! So final inequality is $-1.8x² -1.61x +217.55 ≥255$ which is option C.

Correction Note:

Earlier sign mix-up fixed: $-20.61x +19x = -1.61x$, so the correct inequality is $-1.8x² -1.61x +217.55 ≥255$ which is option C.

Final Answer Adjustment:

C. $-1.8x^2 - 1.61x + 217.55 \geq 255$

Answer:

D. $-1.8x^2 + 21.61x + 217.55 \geq 255$