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Brianna is knitting baby items to sell at a craft fair. She has a total of 1,2801,280 yards of yarn to use for the items. A pair of booties uses 196196 yards of yarn and a cap uses 187187 yards apiece.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of pairs of booties Brianna can knit\newliney=y = the number of caps Brianna can knit\newlineChoices:\newline(A) 187x+196y≤1,280187x + 196y \leq 1,280\newline(B) 196x+187y≤1,280196x + 187y \leq 1,280\newline(C) 187x+196y≥1,280187x + 196y \geq 1,280\newline(D) 196x+187y≥1,280196x + 187y \geq 1,280

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Q. Brianna is knitting baby items to sell at a craft fair. She has a total of 1,2801,280 yards of yarn to use for the items. A pair of booties uses 196196 yards of yarn and a cap uses 187187 yards apiece.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of pairs of booties Brianna can knit\newliney=y = the number of caps Brianna can knit\newlineChoices:\newline(A) 187x+196y≤1,280187x + 196y \leq 1,280\newline(B) 196x+187y≤1,280196x + 187y \leq 1,280\newline(C) 187x+196y≥1,280187x + 196y \geq 1,280\newline(D) 196x+187y≥1,280196x + 187y \geq 1,280
  1. Calculate Yarn Usage: Determine the amount of yarn used for each item. We are given that a pair of booties uses 196196 yards of yarn and a cap uses 187187 yards of yarn. The variables xx and yy represent the number of pairs of booties and caps Brianna can knit, respectively.
  2. Write Inequality: Write an inequality that represents the total amount of yarn used. The total yarn used for booties is 196196 yards per pair times the number of pairs (xx), and the total yarn used for caps is 187187 yards per cap times the number of caps (yy). The sum of these two amounts must be less than or equal to the total yarn available, which is 1,2801,280 yards. So, the inequality is 196x+187y≤1,280196x + 187y \leq 1,280.
  3. Check Against Choices: Check the inequality against the given choices. The correct inequality that matches our calculation is (B)196x+187y≤1,280(B) 196x + 187y \leq 1,280.
  4. Standard Form Check: Ensure that the inequality is in standard form. The standard form for an inequality is Ax+By≤CAx + By \leq C, where AA, BB, and CC are constants. Our inequality 196x+187y≤1,280196x + 187y \leq 1,280 is in standard form, with A=196A=196, B=187B=187, and C=1,280C=1,280.

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