Jillian and Dylan read magazines. Jillian has read 2 magazines and reads 4 more each week. Dylan has read 6 magazines and reads 4 more each week. After how many weeks will they have read the same number of magazines?

Question

Write an equation that represents the number of magazines Dylan has read, y, after x weeks.

Answer 1

To represent the number of magazines Dylan has read after \( x \) weeks, we can start with the number of magazines he has read initially and then include the number he reads each week.

Dylan has read 6 magazines and reads 4 more each week. Therefore, we can write the equation for the number of magazines Dylan has read \( y \) after \( x \) weeks as follows:

\[ y = 6 + 4x \]

Next, we need to write a similar equation for the number of magazines Jillian has read after \( x \) weeks. She has read 2 magazines and also reads 4 more each week:

\[ y = 2 + 4x \]

Now, we want to find the number of weeks \( x \) after which Jillian and Dylan will have read the same number of magazines.

To do this, we set the two equations equal to each other:

\[ 6 + 4x = 2 + 4x \]

Subtract \( 4x \) from both sides:

\[ 6 = 2 \]

This simplifies to a contradiction, indicating that they will never have read the same number of magazines, as they both read at the same rate (4 per week) but started with different quantities.

Thus, they will never reach a point where the number of magazines they have read is equal.