Question

a jewelry designer is making beaded jewelry with the 797 beads she currently has in stock. bracelets use 24 beads and necklaces use 82 beads. select the inequality in standard form that describes this situation. use the given numbers and the following variables. x = the number of bracelets y = the number of necklaces 24x + 82y ≤ 797 24x + 82y ≥ 797 82x + 24y ≤ 797 82x + 24y ≥ 797

Explanation:

Step1: Determine beads used for bracelets

Bracelets use 24 beads each, with \( x \) bracelets, so beads for bracelets: \( 24x \).

Step2: Determine beads used for necklaces

Necklaces use 82 beads each, with \( y \) necklaces, so beads for necklaces: \( 82y \).

Step3: Total beads used and constraint

Total beads used: \( 24x + 82y \). The designer has 797 beads, so total used must be ≤ 797. Thus, \( 24x + 82y \leq 797 \).

Answer:

\( 24x + 82y \leq 797 \)