Abby M. answered • 10/29/20

Ivy League Math and Writing Tutor

Hi Jaila,

This question deals with ratios (also known as proportions). We are told that the violin and the bass have the same ratios / proportions when comparing the body length of the instruments to the entire length of the instruments.

We can write the ratio for the violin first: body length / entire length (sometimes you see ratios written 15:24, but we can alternatively write the ratio as 15 divided by 24, or 15/24)

Since the body length of the violin is 15, and the entire length is 24 inches, we can write the violin ratio as 15/24

Now we're looking to find the body length of the bass, but we only have the total length. The bass ratio would be body length / entire length, but let's call the body length b because we don't know it yet. The ratio for the bass is therefore b/72.

While we don't know what b is, we do know that the ratio for the bass must be the same as the ratio for the violin. In other words, the violin ratio must **equal** the bass ratio.

(15/24) = (b/72)

We can then solve for b by isolating the variable. We need to move anything on the same side of the equation as the b to the other side to isolate the b, which stands for the bass's body length. We do this by multiplying both sides by 72.

(15/24) x 72 = 45

This means that b, the bass's body length, must equal **45 **in order for the ratio of the violin body length vs the violin entire length to be the same as the ratio of the bass body length vs the bass entire length.

Note: If you prefer to work with some simpler numbers, you can think of the violin ratio as a fraction--> 15/24 can be reduced to 5/8 (by dividing both the numerator and the denominator by 3). This will still give us the same answer of 45 by following the steps above (multiplying by the 72 bass entire length).