Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Two students in the same Spanish class, Tristan and Josh, plan to get together after school to make vocabulary flashcards. Tristan started on the project yesterday and has already made 6 flashcards. Josh hasn't started yet. Since Tristan makes 5 flashcards per minute and Josh makes 6 flashcards per minute, Josh will soon have the same number of flashcards. How long will that take? How many flashcards will each student have at that point? In minutes, each student will have flashcards.

Total number of flash cards made by Tristan is equal to Number of flash cards already made by Tristan plus Number of flash card Tristan makes in 1 min multiplied by number of minutes.

framing in equation form we get;

Total number of flash cards made by Tristan = [tex]5+5x[/tex]

Also We can say that;

Total number of flash cards made by Josh is equal Number of flash card Josh makes in 1 min multiplied by number of minutes.

framing in equation form we get;

Total number of flash cards made by Josh = [tex]6x[/tex]

Hence the system of equation used to find the Total number of flash cards made are [tex]\left \{ {{5x+5} \atop {6x}} \right.[/tex].

Now to find the number of minutes when both would have same number of flash cards we will make both the equation equal.

so we get;

[tex]5+5x=6x[/tex]

On solving we get;

Combining like terms we get;

[tex]6x-5x=5\\\\x=5\ mins[/tex]

Hence It would take 5 minutes when both will have same number of flash cards.

To find the number of flash cards each would had at that time we will substitute value of [tex]x=5[/tex] in the system of equations.

so we get;

number of flash cards made by Tristan = [tex]5x+5 = 5\times5+5=25+5=30[/tex]

number of flash cards made by Josh = [tex]6x =6\times 5 =30[/tex]

Hence In 5 minutes, each student will have 30 flash cards.