Answer :
Let A be the amount of hours that Juan can study for Algebra and C the amount of hours that he can study for Chemistry.
Since the total amount of time that he can study is 24 hours, then:
[tex]A+C=24[/tex]Since he will study Algebra three times as long as he will study Chemistry, then:
[tex]A=3C[/tex]Then, a system of equations that represents this set of conditions for the study time, is:
[tex]\begin{gathered} A+C=24 \\ A=3C \end{gathered}[/tex]This system can be solved using the substitution method. Replace A=3C into the first equation and solve for C:
[tex]\begin{gathered} A+C=24 \\ \Rightarrow3C+C=24 \\ \Rightarrow4C=24 \\ \Rightarrow C=\frac{24}{4} \\ \\ \therefore C=6 \end{gathered}[/tex]Replace C=6 into the expression for A:
[tex]\begin{gathered} A=3C \\ \Rightarrow A=3(6) \\ \\ \therefore A=18 \end{gathered}[/tex]Therefore, the system of equations that represents the given situation is:
[tex]\begin{gathered} A+C=24 \\ A=3C \end{gathered}[/tex]And the solution says that Juan has 18 hours to study for Algebra and 6 hours to study for Chemistry.