SOLUTION: Emily is hosting a major after-school party. The principal has imposed two restrictions. First, the total number of people attending (teachers and students combined) must be 56. Se

Question 1202072: Emily is hosting a major after-school party. The principal has imposed two restrictions. First, the total number of people attending (teachers and students combined) must be 56. Second, there must be one teacher for every seven students. How many students and how many teachers are invited to the party?

Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answers: 49 students, 7 teachers

Work Shown:
x = number of students
y = number of teachers

Restrictions:
1. The total number of people attending (teachers and students combined) must be 56.
2. There must be one teacher for every seven students.

x+y = 56 due to restriction #1
x = 7y due to restriction #2

Apply substitution to solve
x+y = 56
7y+y = 56
8y = 56
y = 56/8
y = 7
There must be 7 teachers.
And,
x = 7y
x = 7*7
x = 49
There must also be 49 students.

Check:
x+y = 56
7+49 = 56
49+7 = 56
56 = 56 ... confirmed
and
x = 7y
49 = 7*7
49 = 49 ... confirmed
Both equations are confirmed.

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

        Solve it MENTALLY as shown below.

According to the problem, you can group the attendees in sets in a way that each group contains seven students and one teacher. The number of people in each group is (7+1) = 8; so, the number of groups is 56/8 = 7. 7 groups contain 7*7 = 49 students and 7*1 = 7 teachers. ANSWER. 49 students and 7 teachers.

Solved (mentally)

Good problem to offer it to 4-th grade students, who know nothing about equations,
to develop their skills solving simple problems mentally.

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