Question

The costs of two sound systems were decreased by $10. The original cost of the systems were $90 and $60. Without calculating, which had a greater percent of decrease?

Answer 1

The one with the smaller price ($60).

Explanation:

Let's use some slightly different numbers to figure out a system or rule to look at the question.

Let's say we start with two groups. One group has 2 things and the other group has 100 things. And we take away 1 thing. Which experienced the greater percentage decline?

For the first group, it was `1/2` - it lost 1 thing out of 2 and so that was 50%.

For the second group, it was `1/100` - it lost 1 thing out of 100 things and so was 1%.

So when we take away the same amount from two (or more) groups, the one that will experience the greatest percentage decline is the one that is smaller/smallest.

So let's go to the question. One sound system is $90 and the other is $60 and they are both being discounted by $10. Which has the greater percentage decline? The one with the smaller price.

Answer 2

The $60 purchase had the greater decrease.

Explanation:

`10/60>10/90`

So the $60 purchase had the greater decrease.