Today’s ACT question of the day is a great ratio question to review no matter which test you’re taking.

In a shipment of 1,000 light bulbs, of the bulbs were defective.
What is the ratio of defective bulbs to nondefective bulbs?

When we are dealing with ratios, we have to consider the different types: part-to-part and part-to-whole.

The first ratio, 1/40, is a part-to-whole ratio. It compares the number of defective bulbs to the total number of bulbs.  In this case, the total number of bulbs is 1,000, so we can set up a proportion to find the actual number of defective bulbs:

1/40 = x/1000

In our proportion, all of the “parts” are on top and all of the “wholes” are on the bottom.  You can set up your proportion several different ways, but make sure you don’t mix up your parts and wholes.

After cross-multiplying and then dividing each side by 40, we find that there are 25 defective bulbs.

The ratio they want us to find, defective bulbs to nondefective bulbs, is a part-to-part ratio. We have one part, 25 defective, and we need to find the other part. The whole is 1,000, so 1,000 – 25 = 975 nondefective bulbs. Our ratio is 25/975.

Simplify by dividing the numerator and denominator by 25. The final answer is 1/39.