Question

3. Solve the following application of a system of linear equations.

Answer 1

Answer:

Equations:

$y = 14 + 9 x$ --- Cindy

$y = 10 x$ --- Ruben

Solution to equation:

Time they have the same amount: 14 minutes

Number of cards they have at that time: 140 flashcards

Step-by-step explanation:

Solving (a): Variables and what they represent

The variables to use are x and y

Where x represent the minutes and y represents the number of flashcards in x minutes

Solving (b): System of linear equation

Cindy:

$Existing\ Flashcards = 14$

$Additional = 9$ per minute

Total number of flashcards (y) in x minutes is:

$y = Existing\ Flashcards + Additional * x$

$y = 14 + 9 * x$

$y = 14 + 9 x$

Ruben:

$Rate = 10$ per minute

Total number of flashcards (y) in x minutes is:

$y = Rate * x$

$y = 10 * x$

$y = 10 x$

Solution to Equations:

Time they have the same amount.

To do this, we $equate$ $both$ expressions

i.e.

$10x = 14 + 9x$

Collect Like Terms

$10x - 9x = 14$

$x = 14$

Number of cards they have at that time.

Here, we simply substitute 14 for x in any of the equations.

$y = 10 x$

$y = 10 * 14$

$y = 140$

or

$y = 14 + 9 x$

$y = 14 + 9 * 14$

$y = 14 + 126$

$y = 140$