Question

the probler necessowar factory produces t - shirts and button - down shirts at constant rates. the factory can produce 70 button - down shirts in 2 hours. this table shows how many t - shirts the factory can produce:

which type of shirt does the factory produce at a faster rate?

how many of these shirts can the factory produce in 5 hours?

Explanation:

Step1: Calculate the production rate of T - shirts

The production rate of T - shirts is calculated by dividing the number of T - shirts produced by the time taken. For T - shirts, when 150 are produced in 3 hours, the rate \(r_{T - shirt}=\frac{150}{3}=50\) shirts per hour. When 300 are produced in 6 hours, \(r_{T - shirt}=\frac{300}{6} = 50\) shirts per hour. When 450 are produced in 9 hours, \(r_{T - shirt}=\frac{450}{9}=50\) shirts per hour.

Step2: Calculate the production rate of button - down shirts

For button - down shirts, assume the rate is calculated in the same way. Let's take the first data point (if we assume a linear relationship). But since the problem is mainly about comparing rates (from the first question in the image, which is "Which type of shirt does the factory produce at a faster rate?") and for the second question (number of shirts in 5 hours), we first confirm the rate.
Since the rate of T - shirts is 50 shirts per hour.

Step3: Calculate the number of T - shirts in 5 hours

Using the formula \(N = r\times t\), where \(r = 50\) (shirts per hour) and \(t = 5\) (hours). So \(N=50\times5\)

Answer:

1250