Question

A group of exchange students from Japan went to a convalescent home to sing songs for the seniors and to demonstrate origami. Groups of students and seniors sat together at tables so the students could teach the seniors to fold some origami figures. As it turned out, at each table there was either 1 student and 3 seniors, or 2 students and 4 seniors. There were 23 students and 61 seniors in all. How many tables were being used?

Answer 1

19 tables

Explanation:

Let X represent the number of tables that have 1 student and 3 seniors

Let Y represent the number of tables that have 2 student2 and 4 seniors

Therefore number students total

1X + 2Y =23 (1)

Number of seniors total

3X + 4Y = 61 (2)

Multiply equation (1) by 2 giving

2X + 4Y = 46 (3)

Subtract (3) from (2)

3X + 4Y - (2X+4y) = 61-46

3X + 4Y - 2X -4Y = 15

3X-2X = 15

X = 15

Plugging this value into equation (1) gives

1(15) + 2Y = 23

15 + 2Y = 23

Subtract 15 from both sides

2Y = 23 - 15

2Y = 8

Divide by 2 both sides

Y = 4

Thus total number of tables used = X +Y = 15+4 = 19