Question

The sum of two numbers is 80 and the first number is 20 more than the second. Find the numbers.

Answer 1

Hint: Here, we may represent the second number as a variable and then we can find the first number in terms of the second number. After this, we can form an equation as per the given condition and find the values of both the numbers.

Complete step-by-step answer:
So, at first let us consider that the second number is=x.
Now, since it is given that the first number is 20 more than the second number, we can say that when we add 20 to the second number we may get the first number.
Therefore, we can write:
First number = second number +20
Therefore, first number = x + 20……….(1)
Now, we have the condition from the question that the sum of these two numbers is equal to 80.
Therefore, we can write the following equation:
First number + second number = 80
 $\Rightarrow$ x + 20 + x = 80
$\Rightarrow$ 2x + 20 = 80
$\Rightarrow$ 2x = 80 – 20
$\Rightarrow$ 2x = 60
$\Rightarrow$ $x=\dfrac{60}{2}$
So, x = 30
So, the value of the second number is 30.
Now we may substitute this value of x = 30 in equation (2) and get the value of first number as:
First number = 30 + 20
First number = 50
Hence, the values of the two numbers are 50 and 30.

Note: Students should be careful while making the equations. Here, they should note that the first number exceeds the second number by 20, so we add 20 the second number. Here, mistakes can be made by adding 20 to the first number instead of the second number.