Question

jonah is baking a multi - tiered cake for a friends wedding. an eight - inch cake tier will feed 19 guests and a twelve - inch tier will feed 30 guests. in total, these tiers must feed at least 278 guests, the number attending the wedding. select the inequality in standard form that describes this situation. use the given numbers and the following variables. x = the number of eight - inch tiers y = the number of twelve - inch tiers 30 + x + 19 + y ≥ 278 19x + 30y ≥ 278 30x + 19y ≥ 278 19 + x + 30 + y ≥ 278

Explanation:

Step1: Determine guests per tier type

Eight - inch tiers: Each feeds 19 guests, with \(x\) tiers, so total guests from eight - inch tiers is \(19x\).
Twelve - inch tiers: Each feeds 30 guests, with \(y\) tiers, so total guests from twelve - inch tiers is \(30y\).

Step2: Set up the inequality

Total guests must be at least 278, so the sum of guests from both tiers (\(19x + 30y\)) is greater than or equal to 278. The inequality is \(19x+30y\geq278\).

Answer:

\(19x + 30y \geq 278\)