Question

1. higher order thinking

at a party, the number of
people who ate meatballs
was 11 fewer than \\(\frac{1}{3}\\) of the
total number of people.
five people ate meatballs.

a. write and solve an equation
to find the number of people
at the party. let ( x ) represent
the number of people at
the party.

Explanation:

Step1: Translate the problem into an equation

The number of people who ate meatballs is 11 fewer than $\frac{1}{3}$ of the total number of people. Let \( x \) be the total number of people. So the number of people who ate meatballs is \( \frac{1}{3}x - 11 \). We know that 5 people ate meatballs, so the equation is \( \frac{1}{3}x - 11 = 5 \).

Step2: Solve the equation for \( x \)

First, add 11 to both sides of the equation:
\( \frac{1}{3}x - 11 + 11 = 5 + 11 \)
\( \frac{1}{3}x = 16 \)
Then, multiply both sides by 3 to solve for \( x \):
\( x = 16\times3 \)
\( x = 48 \)

Answer:

The equation is \( \frac{1}{3}x - 11 = 5 \) and the number of people at the party is 48.