Question

Suppose you have developed a scale that indicates the brightness of the sun. Each category in the table is 5 times brighter than the category above it. For example, a day that is dazzling is 5 times brighter than a day that is radiant. How many times brighter is a dazzling day than a dim day if the dim day is 2 and the dazzling day is 5?

Answer 1

Since you are comparing the relative brightness, you simply have to find their ratio to compare how many times larger is the greater value to the other value. The solution is as follows:

Dazzling Day/Dim Day = 5/2 = 2.5

Thus, it means that dazzling day is 2.5 times brighter than dim day.

Answer 2

125 times brighter

Explanation:

If the dazzling day have a value of 5 in your scale, and a dim day, a value of 2, there are 5-2 = 3 category increases between them. Now, every category is 5 times brighter than its immediate predecessor so:

B₃ =5*B₂;

B₄ =5*B₃;

B₅ =5*B₄;

Replacing, we get:

B₅ = 5*(5*(5*B₂));

This is:

B₅ = 5³*B₂;

B₅ = 125*B₂