Question

Brett has long-sleeved shirts and short-sleeved shirts. Some of the shirts are solid colored, and some are patterned. Brett has a total of 30 shirts in all.

The ratio of short-sleeved to long-sleeved shirts is 1:1.
The ratio of solid to patterned shirts is 1:2.
Which statement about Brett's shirts could be true?

Responses

All of the solid shirts are short-sleeved.
All of the solid shirts are short-sleeved.

All of the short-sleeved shirts are solid colored.
All of the short-sleeved shirts are solid colored.

All of the long-sleeved shirts are solid colored.
All of the long-sleeved shirts are solid colored.

All of the patterned shirts are long-sleeved.

Answer 1

All of the solid shirts are short sleeved

Answer 2

Given that Brett has a total of 30 shirts, we can use the provided ratios to determine the number of each type of shirt.

Short-sleeved to Long-sleeved Ratio (1:1):

This means that half of the shirts are short-sleeved and half are long-sleeved.

Short-sleeved = 30/2 = 15 shirts

Long-sleeved = 30/2 = 15 shirts

Solid to Patterned Ratio (1:2):

Out of every 3 shirts, 1 is solid and 2 are patterned.

Given 30 shirts total:

Solid = (1/3) × 30 = 10 shirts

Patterned = (2/3) × 30 = 20 shirts

Now, let's evaluate each statement:

All of the solid shirts are short-sleeved.

There are 10 solid shirts and 15 short-sleeved shirts, so it's possible for all 10 solid shirts to be short-sleeved.

All of the short-sleeved shirts are solid colored.

There are 15 short-sleeved shirts and only 10 solid shirts. So, this statement cannot be true.

All of the long-sleeved shirts are solid colored.

There are 15 long-sleeved shirts and only 10 solid shirts. So, this statement cannot be true.

All of the patterned shirts are long-sleeved.

There are 20 patterned shirts and 15 long-sleeved shirts. So, this statement cannot be true.

So, the only statement that could be true is:

All of the solid shirts are short-sleeved.