Question

A total of 385 people attended the homecoming football game;
everyone present was either a student of the school or a family member. There were 83 more
students than family members present. If the home team won the
game,
how many students and
family were there?

Answer 1

The number of student and family members that attended the homecoming football game are 234 and 151 respectively.

• Let the number of student be S.

• Let the number of family member be F.

Given the following data:

• Total population = 385 people

To calculate the number of student and family members that attended the homecoming football game:

How to solve a word problem.

First of all, we would assign a variable to each group that attended the homecoming football game and then write a system of algebraic equations. Finally, we would solve the system of algebraic equations by using the substitution method.

Translating the word problem into an algebraic expression, we have;

A total of 385 people:

$F+S=385$   .....equation 1.

83 more students than family members:

$S=F+83$   .....equation 2.

Substituting eqn. 2 into eqn. 1, we have:

$F+F+83=385\\\\2F+83=385\\\\2F=385-83\\\\2F=302\\\\F=\frac{302}{2}$

F = 151 family members.

For the students:

$S=F+83\\\\S=151+83$

S = 234 students.

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