Respuesta :
SOLUTION
Given the question in the question tab, the following are the solution step to get the number of books they have altogether.
Step 1: Write the notations for Joseph's and Mike's books
[tex]\begin{gathered} \text{let j represents the number of books Joseph has,} \\ \text{let m represents the number of books Mike has} \end{gathered}[/tex]Step 2: Write the statements in a mathematical form
[tex]\begin{gathered} m=28---\text{statement 1} \\ \frac{1}{3}of\text{ j was given to Mike to have }m+\frac{j}{3}=28+\frac{j}{3} \\ \text{After that, }28+\frac{j}{3}=\frac{2j}{3} \end{gathered}[/tex]Step 3: Solve to get the value of j by using substitution method
[tex]\begin{gathered} \\ m=28+\frac{j}{3} \\ 28+\frac{j}{3}=\frac{2j}{3} \\ \text{ multiply through by 3} \\ 84+j=2j \\ 84=2j-j \\ 84=j \\ j=84 \end{gathered}[/tex]Therefore, Joseph had 84 books initially.
Step 4: Get the number of books they had altogether by summing the number of books for the each of them initially
[tex]\begin{gathered} m=28,j=84 \\ \text{Total}=28+84=112 \end{gathered}[/tex]Hence, they both had 112 books altogether.
