To easily solve ratio problems and to gain a better understanding of the topic in general, it is convenient to know about equivalent ratios.

Equivalent ratios are, in fact, ratios that seem different, are not expressed in the same way but, by simplifying or expanding them, you arrive at exactly the same relationship.

José and Dani have notebooks and pencils. José has $4$ notebooks and $8$ pencils.

The ratio between the notebooks and pencils that Dani has is the same as José's. Dani has $6$ notebooks. We are asked to calculate how many pencils Dani has.

We see that the number of pencils José has is double the number of notebooks he has. Since we already know that the ratio between notebooks and pencils that José and Dani have is identical, we can deduce that Dani has $12$ pencils ($6$ times $2$, so that the number of pencils is double the number of notebooks).

Do you know what the answer is?

Question 1

How many times greater is the length of the radius of the red circle than the length of the radius of the blue circle?

How many times greater is the length of the radius of the red circle, which is 14, than the length of the radius of the blue circle, whose diameter is 7?