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I've been pondering on this question and I realize my understanding of percentages are probably weak so please help guide me through. Let's say 9th grade is 70% girls and tenth grade is 30% girls. If 40% of all ninth and tenth grade students are girls, what is the ratio of the number of 9th grade students to 10th grade students. So this is from my understanding: I think 70 out of 100 students are girls in gr 9, and 30 out of 100 girls in gr 10. Then this means total number of students in gr 9 and 10 would be 200 so 40% of that is 80 students. But I don't know where to go from here and I feel like it doesn't add up...Please explain what is wrong with my thinking and how I should be thinking! Thank you!!

Star S
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  • Percentages like 40% here can represent things like 40 out of 100. But they don't always have to - notice that 20 out of 50 is also "40%". So there's no reason why total number of students in each year has to be 100! In fact, it turns out that both aren't 100 (if you work through the problem, you'll find that the ratio is not 1, so the number of students in each year is not equal) – John Doe May 18 '19 at 18:56

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The problem with your answer is that you're implicitly assuming the ratio of students in the two classes to be $1:1$. (Are you able to see that?)

Here's how to go about it:

Let the number of students in $9^{th}$ grade be $x$ and $10^{th}$ grade be $y$.

$$G_9 = 0.7x$$

$$G_{10} = 0.3y$$

$$G = G_9 + G_{10} = 0.4(x+y)$$

Notation:

$G_9$: girls in $9^{th}$ grade.

$G_{10}$: girls in $10^{th}$ grade.

$G$: Total girls

Solve for $\frac{x}{y}$!

Vizag
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