How do you solve this it's hard

When it rains, every student in Margo's school brings a raincoat, an umbrella, or both. And 10% of the students bring both. The total number of umbrellas brought is equal to twice the number of raincoats.

What percent of the students bring an umbrella only? Explain your solution in complete sentences.

Guest Apr 26, 2023

#1**0 **

*When it rains, every student in Margo's school brings a raincoat, an umbrella, or both. And 10% of the students bring both. The total number of umbrellas brought is equal to twice the number of raincoats.*

*What percent of the students bring an umbrella only? Explain your solution in complete sentences.*

So 90% brought only one thing

Twice as many are umbrellas,

so it looks like **60% brought an umbrella** and 30% brought a raincoat.

Have I done something wrong? That seemed too easy.

_{.}

Guest Apr 27, 2023

#2**0 **

Yes, something doesn't add up because in your argument, you are stating that 60% of people ONLY brought umbrellas and 30% ONLY brought raincoats but the question is saying that the TOTAL number of umbrellas brought(which includes students who brought not ONLY umbrlelas, but also raincoats) is twice the amount of people who brought raincoats.

Voldemort Apr 27, 2023

#5**0 **

**Voldemort**

I couldn't understand what you were trying to say, until late last night – while I was brushing my teeth, if it matters – and then it dawned on me.

You were trying to tell me that the 2 to 1 ratio of umbrellas to raincoats has to take into account the umbrellas and raincoats of the students who brought both. What I did wrong was to dismiss the number of umbrellas and raincoats brought by students who brought both. A clumsy mistake. No wonder the darn thing seemed too easy.

I looked this question up, and I found it answered by CPhill. I don't know if you recognize that name, but he was a Moderator on this site for like forever. He hasn't been around for a while. I hope he's just taking a break, and not gone permanently.

This is the URL of Chris' answer: https://web2.0calc.com/questions/on-a-rainy-day-every-kid-at-margo-s-school-brings-a-raincoat

It's the same problem, except that it has 8% of students bringing both an umbrella and a raincoat, rather than 10%.

I would have copied Chris' calculations and pasted the entire thing in, except that thread had a dissenting opinion. That other opinion is worth taking a look at, but I think Chris is correct. A fellow can go broke in a hurry, betting against CPhill.

_{.}

Guest Apr 27, 2023

#6**0 **

What we need is to separate the 90% into some r (raincoats) and u (umbrellas)

2r+20=u+10

2r+10=u

Since u+r=90, we can add r to both sides.

3r+10=u+r

3r+10=90

3r=80

r=80/3

Then u = 190/3

If we add 30/3 to both u and r we get

u=220/3

r=110/3

So u is twice r.

Then, if 190/3% people brought umbrellas only, than 63.3333% of the people only brought umbrellas. You could also put 63 1/3%. Then, the number of students must be a multiple of 300 for this to work.

gb1falcon May 2, 2023