Question

In a room there are some students and gauvas. If each student eats four gauvas,then one student is left alone without having any gauva. If each student eats three gauvas, then one gauva is left. Write the pair of equations to find the number of students and gauvas.

Answer 1

The pair of equations to find the number of students and guavas are

(x-1)*4=y

x*3=y-1

1. Lets say there are x students and y number of guavas.

2. Initially if each student eats 4 guavas then one student is left without any guava. That means x-1 students ate all the guavas. Mathematically

(x-1)*4=y

3. Now if each student eats 3 guavas then one guava is left without any student. That means x students ate all the guavas except one. Mathematically

x*3=y-1

4. Solving the two equations by replacing y by (x-1)*4 from first equation.

3x=4x-4-1

x=5

no. of students =5

y=(x-1)*4=4*4=16.

no. of guavas=16