Question

1. lara is baking cupcakes for the bake sale. she needs at least 96 cupcakes and no more than 120 cupcakes. her baking pan holds 12 cupcakes. if she already baked 12 cupcakes, how many more pans of cupcakes does she need to bake?

she needs to bake ( 8 leq x leq 10 ) more pans of cupcakes.
she needs to bake ( 9 leq x leq 11 ) more pans of cupcakes.
she needs to bake ( 10 leq x leq 12 ) more pans of cupcakes.
she needs to bake ( 7 leq x leq 9 ) more pans of cupcakes.

Explanation:

Step1: Define variables and inequalities

Let \( x \) be the number of more pans. Total cupcakes: \( 12 + 12x \). She needs at least 96 and at most 120, so \( 96 \leq 12 + 12x \leq 120 \).

Step2: Solve left inequality

Subtract 12: \( 96 - 12 \leq 12x \) → \( 84 \leq 12x \). Divide by 12: \( 7 \leq x \).

Step3: Solve right inequality

Subtract 12: \( 12x \leq 120 - 12 \) → \( 12x \leq 108 \). Divide by 12: \( x \leq 9 \).

Step4: Combine solutions

\( 7 \leq x \leq 9 \).

Answer:

She needs to bake \( 7 \leq x \leq 9 \) more pans of cupcakes. (The last option: She needs to bake \( 7 \leq x \leq 9 \) more pans of cupcakes.)