Question

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:

Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

Answer 1

Solve this problem, form two linear equations using the given information and solve them using the elimination method. Nuri's age is 80 years and Sonu's age is 30 years.

Step-by-step explanation:

To solve this problem, let's first assign variables to the ages of Nuri and Sonu. Let N represent Nuri's age and S represent Sonu's age.

From the given information, we can form two linear equations:

1. Equation 1: N - 5 = 3(S - 5)
2. Equation 2: N + 10 = 2(S + 10)

Simplifying the equations:

1. Equation 1: N - 5 = 3S - 15
2. Equation 2: N + 10 = 2S + 20

Now, we can solve these equations using the elimination method.

Multiplying Equation 1 by 2, we get:

1. 2(N - 5) = 2(3S - 15)
2. 2N - 10 = 6S - 30

Adding the equations:

1. (2N - 10) + (N + 10) = (6S - 30) + (2S + 20)
2. 3N = 8S

Now, we can substitute one of the variables to solve for the other:

1. Using Equation 1: N - 5 = 3S - 15
2. N = 3S - 10

Substituting N = 3S - 10 into 3N = 8S:

1. 3(3S - 10) = 8S
2. 9S - 30 = 8S
3. S = 30

Substituting S = 30 into N = 3S - 10:

1. N = 3(30) - 10
2. N = 80

Therefore, Nuri is 80 years old and Sonu is 30 years old.