# 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 1st 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.