Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Question

Two students in the same Spanish class, Allie and Hunter, plan to get together after school to make vocabulary flashcards. Allie started on the project yesterday and has already made 8 flashcards. Hunter hasn't started yet. Since Allie makes 5 flashcards per minute and Hunter makes 9 flashcards per minute, Hunter will soon have the same number of flashcards. How long will that take? How many flashcards will each student have at that point? In how many minutes, each student will have how many flashcards.

Answer 1

Let t be the time in minutes

Let a be the number of cards Allie makes.

Let h be the number of cards Hunter makes.

a = 5t + 8

h = 9t

Need to know when a=h

5t+h = 9t

Just solve for t to find how much time that it will take for Hunter to catch up with Allie in minutes. Then substitute that value into either Allie's expression or Hunter's expression to get the number of cards each made.

Answer 2

The amount of flashcards Allie makes is 5 per minute so after 1 minute, she has 5 made, after two minutes she has 10 made, etc. So to get the number of flashcards she has made, multiply 5 by the number of minutes (t). But she starts with 8 so the amount she has is 5t + 8.

The amount Hunter has is just 9t (since he hadn't started yet). You want them to be the same so:

5t + 8 = 9t

Can you solve for "t"?