A chess team consists of 14 boys and 8 girls. (i) What is the ratio of number of boys to number of girls in the chess team? (ii) What is the ratio of the girls to the total number of participants in the team? Express the ratio in the simplest form.
Answers
Answer:
(i) Boys = 14
Girls = 8
Boys : Girls = 14 : 8
= 7 : 4
(ii) Girls = 8
Total participants = 22
Girls : Total participants = 8 : 22
= 4 : 11
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Step-by-step explanation:
A ratio compares two quantities in terms of multiplication. For example, suppose that there are 10 boys and 15 girls in a classroom. One way, not using ratios, to compare these quantities would be to say that there are 5 more girls than boys in the classroom. To employ a ratio, we say that the ratio of boys to girls is 10 to 15, or 2 to 3. In other words, for every 2 boys in the classroom, there are 3 girls.
Writing a Ratio
You can express a ratio using a colon or a fraction: namely, as
The fraction notation is usually superior for ratios with two elements, but if you have a ratio with three elements, the colon notation is usually superior: for example, 10:15:19.
In the classroom example, many other ratios can be made. The number of boys out of the total number of students is 10/25. The number of girls out of the total number of students is 15/25. And 15/10 is the ratio of the number of girls to the number of boys.
Ratios, being fractions, can sometimes be reduced. For example, the ratio of boys to girls in our hypothetical classroom is 10/15. So, we would be correct if we said that the ratio of boys to girls in our hypothetical classroom is 2:3, or two boys for every 3 girls.
Notice that knowing a ratio doesn’t tell us the actual numbers involved. If the ratio of boys to girls is 2:3 or 2/3, we don’t know whether the actual number of boys and girls is 2 and 3, 10 and 15, or 200 and 300. This fact appears frequently on GMAT questions