# 30MSC 2023 #9: Proportionately (Further Applications)

Among the least favored topics in Mathematics are **ratio **and **proportion, **although their applications are wide and far-reaching. A **ratio** is the simplest way of comparing two quantities and the expression of the **equality of two ratios** is called a **proportion**.

A proportion is often expressed in colon format, **a:b = c:d**. To solve any unknown quantity in the proportion, we were taught that the **“product of the means is equal to the product of the extremes”** or *bc = ad*.

It may also be in fraction form, **a/b = c/d**, in which case **cross multiplication** is used to get the equality **ad = bc. **From here, we can solve for any unknown. **b = ad/c **or it may be** c = ad/b.**

However, students should be able to solve ratio problems mentally without even knowing this formula as in the case of this combined ratio problem given in the 1^{st} International Vedic Mathematics Olympiad(IVMO 2021).

“**A box contains red, blue and yellow counters. The ratio of red to blue is 3 : 5 and the ratio of blue to yellow is 7 : 9. There are 90 yellow counters in the box. How many red counters are there?**”

The ratio of blue to yellow is 7 : 9, which means that for every 9 yellow counters, there are 7 blue ones. Since there are 90 (9 x 10) yellows, there must be 70 (7 x10) blues. And since the ratio of red to blue is 3:5 and there are 70 (7 x 10 or 7 x 2 x 5 = 14 x 5), then there must be (14 x 3 = 42) red counters.

0ther applications of Proportionately in ratio Problems, cubing and in geometry are discussed in Chapter 9 of our e-book, **30 Master Strategies in Computing, Volume I.** The rewritten version will be available before the end of the year. Follow us on our Facebook page, MATH-Inic Philippines at https://www.facebook.com/MATHInicPhils to see tomorrow’s **30MSC 2023 #: Magic Numbers 9 and 11.**