Question

One number is twice the other number. If 10 is subtracted from both the number, one of the new
numbers becomes 2.5 times the other number. find the numbers ​

Answer 1

The first number is 60 and the second number is 30 according to the given equations.

Let us represent the two numbers in the problem statement using variables. Let the two numbers be assumed as variables 'x' and 'y' with 'x' being the greater number than 'y'.

Forming Equation 1 :

It is stated that one number is twice the other number. As, we assumed the larger number to be 'x', the equation formed is :

                $x = 2 * y$

Forming Equation 2 :

It is stated that subtracting 10 from both numbers leads to one number becoming 2.5 times the other number. As, we assumed the larger number to be 'x', the equation formed is :

                $(x-10) = 2.5 * (y-10)$

Solving the two linear equations for the 2 variables 'x' and 'y' using the Substitution Method :

( we substitute the value of the larger variable 'x' from Equation 1 and put it in Equation 2 )

                   $(x-10) = 2.5*(y-10)\\\\(2y-10) = 2.5*(y-10)\\\\2y-10 = 2.5y-25\\\\25 - 10 = 2.5y - 2y\\\\15 = 0.5y\\\\y = 15 * 2\\\\y = 30$

Now, the other variable i.e. 'x' can be obtained as :

                   $x = 2*y\\\\x = 2*30\\\\x = 60$

Hence, the two numbers are 60 and 30.

To learn more about Substitution Method, visit

https://brainly.in/question/19563391

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