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
[tex]\begin{gathered} largernumber=l \\ smallernumber=s \end{gathered}[/tex]The sum of two numbers is 48. This can be represented mathematically as below:
[tex]l+s=48======\text{equation 1}[/tex]Their difference is 22. This can be represented mathematically as below:
[tex]l-s=22====\text{equation 2}[/tex]Combine equation 1 and equation 2 as below:
[tex]\begin{gathered} l+s=48========\text{equation 1} \\ l-s=22========\text{equation 2} \end{gathered}[/tex]Add equation 1 and 2 to eliminate s
[tex]\begin{gathered} So, \\ 2l=70 \\ \text{divide both sides by 2} \\ \frac{2l}{2}=\frac{70}{2} \\ l=35 \end{gathered}[/tex]Substitute l = 35 in equation 1
[tex]\begin{gathered} l+s=48 \\ s=48-l \\ s=48-35 \\ s=13 \end{gathered}[/tex]Hence,
The larger number, l = 35
The smaller number, s = 13
