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.
Good work!
Complete the table below with the number of magazines, y, that Jiro has read after 3, 5, and 7 weeks. You can solve on paper and then enter your answer on Zearn.
y=5+5x

Weeks (x) Magazines (y)
3
5
7
Nice!
Next, graph the points you just found on the coordinate plane to show the relationship between x, the number of weeks, and y, the number of magazines Jiro has read.
Weeks (x) Magazines (y)
3 20
5 30
7 40
You got it!
Now, consider Camden. Write an equation that represents the number of comic books Camden has read, y, after x weeks.

Answer 1

To write an equation for the number of magazines Camden has read after \(x\) weeks:

Camden starts with 10 magazines and reads 5 more each week, so the equation is:

\[ y = 10 + 5x \]

where:

• \(y\) is the total number of magazines Camden has read after \(x\) weeks,
• \(10\) is the number of magazines he has already read,
• \(5\) is the number of magazines he reads each week.

Now, let's compare the two equations, the one for Jiro and the one for Camden:

• Jiro's equation: \(y = 5 + 5x\)
• Camden's equation: \(y = 10 + 5x\)

Finding When They Have Read the Same Number of Magazines

To find when Camden and Jiro have read the same number of magazines, we can set their equations equal to each other:

\[ 10 + 5x = 5 + 5x \]

Subtracting \(5x\) from both sides gives:

\[ 10 = 5 \]

Since this is not a valid equation, it shows they will never have read the same number of magazines because Camden always starts with a higher number of already read magazines.

In Summary:

• Camden's equation for the total number of magazines read after \(x\) weeks is: \[ y = 10 + 5x \]

Thus, we know they will always differ by 5 magazines after any number of weeks.