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Studying for a test? Prepare with these 9 lessons on Ratios, rates, proportions.

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# Ratio word problem: boys to girls

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In a language class, the girl to boy ratio is 5 to 8. So for every 5 girls, we have 8 boys. If there are a total of 65 students, how many girls are there? So this is interesting. They give us the ratio of girls to boys. But then they want us to think about how many girls there are given that there are 65 total students. So what we really want to think about is not just the ratio of girls to boys – we want to think about the ratio of girls to total students. So how can we figure out what this ratio's going to be? Well the girl-to-boy ratio gives us a good clue. If there are 5 girls for every 8 boys, how many total students are there going to be for every 5 girls? Well for every 5 girls, you're going to have 5 girls and 8 boys. You're going to have 13 total students. So I just added the 5 and the 8 right over here. The ratio of girls to total students is 5 to 13. One way of thinking about it is if you were to evenly divide the students into groups of 13, every group of 13 students would have 5 girls. Now, I think we're ready to figure out how many total girls there are. Because they tell us that there are 65 students. So, we don't just have one group of 13, we have 65 students. And how many groups of 13 are in 65? Well to go from 13 to 65, you have to multiply by 5. 5 × 10 is 50 and 5 × 3 is 15. Right. So, 13 × 5 is 65. So essentially, one way you could view it is you have 5 groups of 13. So if you have 5 groups of 13, each of those are going to have 5 girls. Multiply by 5, and you're going to have 25 girls. So for every 65 students, you're going to have 25 girls, given the information that has been given.