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

Answer 1

Let's start by defining the number of magazines each person has read after \(x\) weeks.

• Camden has read 10 magazines and reads 5 more each week, which can be represented as: \[ \text{Magazines read by Camden} = 10 + 5x \]

• Jiro has read 5 magazines and also reads 5 more each week, which can be represented as: \[ \text{Magazines read by Jiro} = 5 + 5x \]

Now, to find out after how many weeks they will have read the same number of magazines, we need to set the two equations equal to each other: \[ 10 + 5x = 5 + 5x \]

To solve for \(x\), we can simplify the equation. First, let's subtract \(5x\) from both sides: \[ 10 = 5 + 0 \] This simplifies to: \[ 10 = 5 \] Since this is not a correct statement, it indicates that Camden and Jiro will never have read the same number of magazines.

The equations can be interpreted as showing that Camden starts off ahead and continues to maintain that lead because they both read the same number of magazines each week. Therefore, there will be no points in time where they have read the same amount.

Summary:

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

• Camden and Jiro will never read the same number of magazines.