Question

The sum of two numbers is 48. Their difference is 22. Find the numbers.AnswerHow to enter your answer (opens in new window)larger number:smaller number:

Answer 1

Given: The sum of two numbers is 48. Their difference is 22

To Determine: The value of the larger and the smaller number

Represent the larger and the smaller number with unknowns

`\begin{gathered} largernumber=l \\ smallernumber=s \end{gathered}`

The sum of two numbers is 48. This can be represented mathematically as below:

`l+s=48======\text{equation 1}`

Their difference is 22. This can be represented mathematically as below:

`l-s=22====\text{equation 2}`

Combine equation 1 and equation 2 as below:

`\begin{gathered} l+s=48========\text{equation 1} \\ l-s=22========\text{equation 2} \end{gathered}`

Add equation 1 and 2 to eliminate s

`\begin{gathered} So, \\ 2l=70 \\ \text{divide both sides by 2} \\ (2l)/(2)=(70)/(2) \\ l=35 \end{gathered}`

Substitute l = 35 in equation 1

`\begin{gathered} l+s=48 \\ s=48-l \\ s=48-35 \\ s=13 \end{gathered}`

Hence,

The larger number, l = 35

The smaller number, s = 13