Sheila and Judy read magazines. Sheila has read 10 magazines and reads 5 more each week. Judy has read 5 magazines and reads 5 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 Judy has read, y, after x weeks.

Answer 1

To find when Sheila and Judy will have read the same number of magazines, let’s define the equations for the number of magazines each person has read after \( x \) weeks.

Sheila's Magazines:

• Sheila starts with 10 magazines and reads 5 more each week.
• After \( x \) weeks, the total number of magazines she has read can be represented as: \[ \text{Sheila's magazines} = 10 + 5x \]

Judy's Magazines:

• Judy starts with 5 magazines and also reads 5 more each week.
• After \( x \) weeks, the total number of magazines she has read can be represented as: \[ \text{Judy's magazines} = 5 + 5x \]

Now, we need to set the two expressions equal to each other to find when they will have read the same number of magazines: \[ 10 + 5x = 5 + 5x \]

Next, we can solve for \( x \). First, subtract \( 5x \) from both sides: \[ 10 = 5 + 0 \]

Then, simplify the equation: \[ 10 = 5 \]

This equation suggests that it is impossible for Sheila and Judy to read the same number of magazines. Therefore, there is no solution for \( x \).

To specifically answer your question:

• The equation that represents the number of magazines Judy has read after \( x \) weeks is: \[ y = 5 + 5x \]

However, both expressions indicate that they will never equal each other, thus they will never have read the same number of magazines.