Question

The sum of two numbers is 55. The larger number is 23 more than the smaller number. What are the numbers?Larger number - Smaller number -

Answer 1

Step-by-step explanation

This is a word problem leading to a simultaneous equation

Let the small number be x

Let the large number be y

so we will have

`\begin{gathered} x+y=55 \\ y=x+23 \end{gathered}`
`\begin{gathered} solving\text{ for x and y} \\ \\ \mathrm{Substitute\:}y=x+23 \\ x+x+23=55 \\ \\ 2x=55-23 \\ 2x=32 \\ x=16 \\ \\ y=55-16=39 \\ y=39 \end{gathered}`

Therefore

The larger number is 39

Smaller number is 16