Can someone help me?

lillybeth

lillybeth

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The ratio of boys to girls at a school is 12 to 13. If 300 students attend the school, how many are boys?

How do I figure this out? thanks!
 
lillybeth said:
The ratio of boys to girls at a school is 12 to 13. If 300 students attend the school, how many are boys?

How do I figure this out? thanks!
Click to expand...
Ratios are a DIFFERENT way to express RELATIVE values.

\(\displaystyle \dfrac{number\ of\ boys\ in\ the\ school}{number\ of\ girls\ in\ the\ school} = \dfrac{12}{13}.\)

That statement tells you NOTHING about how many students there are in the school or even how many boys and girls there are. It allows you to compare RELATIVELY the number of boys to the number of girls in schools of different size.

Now let's say that you want to know how many boys and girls there are in that school and you know that 300 students attend.

For every 12 boys there are 13 girls. But that means that there are 12 boys for every 25 students.

\(\displaystyle \dfrac{12\ boys}{25\ students} * 300\ students = 144\ boys.\)

But that means there are 300 - 144 = 156 girls. Let's check.

\(\displaystyle \dfrac{144}{156} = \dfrac{12 * 12}{12 * 13} = \dfrac{12}{13}.\)

Quite frankly, I find percents easier to work with than ratios.

If they had said that boys comprised 48% of the students I could have got the percentage of girls by subtracting 48 from 100, which even I can do in my head.

\(\displaystyle And\ 48\ percent\ of\ 300\ students = \left(48 * \dfrac{1}{100}\right) * 300 = 3 * 48 = 144\ boys.\)

But ratios are used frequently so you need to know them even though I, the great and glorious Jeff, prefer percents for relative measurements.
 
Ratio Word Problem

lillybeth said:
The ratio of boys to girls at a school is 12 to 13. If 300 students attend the school, how many are boys?

How do I figure this out? thanks!
Click to expand...



12x/13x = boys/girls

Let 12x = the number of boys

12x + 13x = 300

25x = 300

x = 300/25

x = 12

Can you take it from here?
 
JeffM said:
Ratios are a DIFFERENT way to express RELATIVE values.

\(\displaystyle \dfrac{number\ of\ boys\ in\ the\ school}{number\ of\ girls\ in\ the\ school} = \dfrac{12}{13}.\)

That statement tells you NOTHING about how many students there are in the school or even how many boys and girls there are. It allows you to compare RELATIVELY the number of boys to the number of girls in schools of different size.

Now let's say that you want to know how many boys and girls there are in that school and you know that 300 students attend.

For every 12 boys there are 13 girls. But that means that there are 12 boys for every 25 students.

\(\displaystyle \dfrac{12\ boys}{25\ students} * 300\ students = 144\ boys.\)

But that means there are 300 - 144 = 156 girls. Let's check.

\(\displaystyle \dfrac{144}{156} = \dfrac{12 * 12}{12 * 13} = \dfrac{12}{13}.\)

Quite frankly, I find percents easier to work with than ratios.

If they had said that boys comprised 48% of the students I could have got the percentage of girls by subtracting 48 from 100, which even I can do in my head.

\(\displaystyle And\ 48\ percent\ of\ 300\ students = \left(48 * \dfrac{1}{100}\right) * 300 = 3 * 48 = 144\ boys.\)

But ratios are used frequently so you need to know them even though I, the great and glorious Jeff, prefer percents for relative measurements.
Click to expand...

This was one of the most elegant answers to the question which I was looking for. The steps were pretty much self explanatory. Just factoring sometimes becomes a tedious job. ;)
 
This was one of the most elegant answers to the question which I was looking for. The steps were pretty much self explanatory. Just factoring sometimes becomes a tedious job. ;) Tutoring
 
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