question_answer 5)

                Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

Answer:

                Let the smaller number be \[x\]. Then, the larger number \[=x+15\] \[\because \]     Sum of two numbers is 95 \[\therefore \] \[x+(x+15)=95\] \[\Rightarrow \]               \[2x+15=95\] \[\Rightarrow \]               \[2x=95-15\]                      | Transposing 15 to RHS \[\Rightarrow \]               \[2x=80\] \[\Rightarrow \]               \[x=\frac{80}{2}=40\]                     | Dividing both sides by 2 \[\Rightarrow \]               \[x+15=40+15=55\] Hence, the desired numbers are 40 and 55. Check: 55 = 40 + 15          | as desired \[40+55=95\].