A jewelry designer is making beaded jewelry with the 980 beads she currently has in stock. Bracelets use 34 beads and necklaces use 76 beads.

Question

Write 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

Answer 1

To formulate the inequality based on the given information, we need to express the total number of beads used for the bracelets and necklaces in relation to the total number of beads available.

We have:

• Each bracelet uses 34 beads, so the total number of beads used for \( x \) bracelets is \( 34x \).
• Each necklace uses 76 beads, so the total number of beads used for \( y \) necklaces is \( 76y \).

The total number of beads spent on bracelets and necklaces should not exceed the total number of beads available, which is 980. Thus, we can write the inequality as:

\[ 34x + 76y \leq 980 \]

This inequality is in standard form.