I can't figure this one out. What's the answer, and how would I find it?
In a certain class, 4/7 of the students are boys, and the ratio of the students older than or equal to 10 years to the students less than 10 years old is 2:3. If 2/3 of the girls are less than 10 years old, what fraction of the boys are older than or equal to 10 years?
The easiest way to solve this problem is to start with a hypothetical number of kids that's divisible by 7. From the question, we know that 4/7 of the class is made up of boys and 3/7 is made up of girls. Since we started with 70, we can say that 40 of the kids are boys in our hypothetical class, and 30 are girls. Of the girls, we know that 2/3 are younger than 10 are 1/3 are 10 or older. This means that there are 10 girls older than 10 and 20 girls younger than 10.
Now, we can use the variable x as a stand-in for the number of boys that are 10 years old or older. The number of boys who are younger than 10 can be represented by the expression 40-x (subtract x from the total number of boys in the class). To find x, we would use the 2:3 ratio. Plugging in the values we just found, this means that x + 10 divided by (40-x) + 20 should be equivalent to 2/3.
Simplified, the expression looks like (x+10)/(60-x) = 2/3. Then, x+10 = 40 - (2/3)x, and (5/3)x = 30. With this expression, x comes out to be 18. Now remember, we're looking for the fraction of the boys that are older than or equal to 10 years, so 18 isn't the final answer. Since our original class had 40 boys total, the fraction we are looking for is 18/40, which can be reduced to our final answer, 9/20.