The problem asks to identify which of the ratios 20:16, 13:9, and 32:36 are equivalent to 15:12.

1. Problem Description

The problem asks to identify which of the ratios 20:16, 13:9, and 32:36 are equivalent to 15:

1

2.

2. Solution Steps

First, simplify the given ratio 15:12 by dividing both numbers by their greatest common divisor (GCD), which is

3. $15 \div 3 = 5$

$12 \div 3 = 4$

So, the simplified ratio is 5:

4.

Now, let's simplify the given options:

* 20:16: The GCD of 20 and 16 is

4. $20 \div 4 = 5$

$16 \div 4 = 4$

So, the simplified ratio is 5:

4. * 13:9: 13 and 9 have no common factors other than

1. So the ratio 13:9 is already in simplest form.

* 32:36: The GCD of 32 and 36 is

4. $32 \div 4 = 8$

$36 \div 4 = 9$

So, the simplified ratio is 8:

9.

Compare the simplified ratios to 5:

4.

* 20:16 simplifies to 5:4, which is equivalent to 15:

1

2. * 13:9 is not equal to 5:4, so it is not equivalent to 15:

1

2. * 32:36 simplifies to 8:9, which is not equal to 5:4, so it is not equivalent to 15:

1

2.

3. Final Answer

The only ratio equivalent to 15:12 is 20:16.