Question

The sum of two numbers is 85. If one number exceeds the other by 25, find the two numbers.

Answer 1

Hint: We will first let the two numbers be \[a\] and \[b\]. As the sum of two numbers is given as 85 so, we will form the equation using it. Also, it is given in the question that if one number exceeds the other by 25 then we will get \[b = a + 25\] which gives us the second equation. Now, we will substitute the equation 2 in 1 and determine the value of \[a\] and using the value of \[a\] we can evaluate the value of \[b\] and hence get the two numbers.

Complete step by step answer:

We will first let the two numbers be \[a\] and \[b\].
Now, we are given that the sum of two numbers is 85,
Hence, we get,
\[ \Rightarrow a + b = 85\]------(1)
Now, as the question says that the one numbers exceeds the other by 25,
Thus, we have,
\[ \Rightarrow b = a + 25\]------(2)
Now, we will use the substitution method, that is we will substitute the value of \[b\] from equation (2) in equation (1) and simplify,
We get,
\[
   \Rightarrow a + a + 25 = 85 \\
   \Rightarrow 2a = 85 - 25 \\
   \Rightarrow 2a = 60 \\
   \Rightarrow a = 30 \\
 \]
Hence, we get the value of one number as 30.
Next, we will find the value of \[b\] by substituting the value of \[a\] in equation (2).
Thus, we get,
\[
   \Rightarrow b = 30 + 25 \\
   \Rightarrow b = 55 \\
 \]
Hence, the two numbers are 30 and 55.

Note: We can simplify the equations by using the elimination method also to determine the values as by eliminating the one variable and solve the second variable and then substitute the value in that. As the sum is given so, we have formed the equation from it and for the second equation we have used the given statement from the question. Substitute the values carefully while solving the equations. It is necessary to form two equations to find the numbers. Simplify the equations properly to avoid the calculation mistakes.