Question

Solve the following problems using two variables
(i) The sum of two numbers is 97. If the greater number is divided
by the smaller, the quotient is 7 and the remainder is 1. Find
the numbers.​

Answer 1

Solution:-

Let the two numbers be x and y, where x is the larger no.

x+y=97 ...(1)

As per the given condition,

x=7y+1 ...(2)

Substitute eq(2) in eq(1) we get

7y+1+y=97

8y=96

y=12

∴x=7(12)+1=85

EXPLAINED:-

• Here we will assume the two numbers be x and y in which x be the larger. Then we will form the linear equations in two variables using the given information and then solve for the values of x and y to get the desired solution

• The linear equation in two variables is the equation which contains two variables and each variable has power as Also, the dividend in remainder theorem is the number which gets divided and the divisor is the number from which the dividend gets divided.

Answer 2

Answer:

85 and 12

Step-by-step explanation:

Let the two numbers be x and y, where x is the larger no.

x+y=97  ...(1)

As per the given condition,

x=7y+1     ...(2)

Substitute eq(2) in eq(1) we get  

7y+1+y=97

8y=96

y=12

∴x=7(12)+1=85