SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given Principal
[tex]\begin{gathered} Kevin=100\text{ dollars} \\ Joseph=100\text{ dollars} \end{gathered}[/tex]STEP 2: Determine the interests for both accounts
For Kevin
[tex]\begin{gathered} 5\text{ dollars every month} \\ Interest\text{ in 2 months will be:} \\ 2\times5=10\text{ dollars} \end{gathered}[/tex]For Joseph
[tex]\begin{gathered} 3\%\text{ of \$100 per month will be:} \\ \frac{3}{100}\times100=3\text{ dollars per month} \\ Interest\text{ in 2 months will be:} \\ 2\times3=6\text{ dollars} \end{gathered}[/tex]STEP 3: Choose the account that will have more money in it after 2 months
[tex]\begin{gathered} Kevin^{\prime}s\text{ account after 2 months}\Rightarrow100+10=110\text{ dollars} \\ Joseph^{\prime}s\text{ account after 2 months}\Rightarrow100+6=106\text{ dollars} \end{gathered}[/tex]Hence, Kevin's account will have more money in it after 2 months
STEP 4: Calculate the number of months when they will have same amount of money in them
[tex]\begin{gathered} For\text{ Kevin, the equation for amount will be:} \\ 100+5x \\ \text{For Joseph, the equation for amount will be:} \\ 100\times1.03^x \\ Where\text{ x is the number of months.} \end{gathered}[/tex]For them to have same amount, this means that:
[tex]\begin{gathered} 100+5x=100\times1.03^x \\ \text{By simplification,} \\ x=33 \end{gathered}[/tex]Hence, they will have same amount in the accounts after 33 months.
