Can someone please solve this easy math problem for me?

[Lumia925]

There's enough food to last 50 labors for 16 days. After 10 days, 10 more labors join the company. How long will the food last?


Please show your work and explain in brief. This is a homework question of a 12 years old kid- I'm 33 and yet can't figure out how to solve this- it's quite embarrassing

 

[Multipack]

Isn't it just 20% less than 6 days? So, 4.8 days?

 

[USAFRet]

You have 800 "food units" (50*16)
After 10 days, you have consumed 500. Leaving 300 for the rest of the time.
Adding 10 people brings that time down to 5 days (300/60=5), instead of the original 6 days.

So adding those 10 people reduces the total time to 15 days vs the original 16.

 

[elbert]

The 10 days you count straight. Now adding 10 more to 50 is 120% increase for last 6 days. Then 120% of 5 is 6. The answer is 15 days.

 

[Multipack]

Isn't it how long the rest of the food will last though?

 

[ko888]

The question is ambiguous. Did the company start off with 50 laborers or less than 50 laborers or more than 50 laborers?

When answering the question you should state your assumptions, if any.

 

[Lumia925]

Thanks Air Force and Geofelt. Thanks to Multipack too, for trying to help.
This makes perfect sense now
Geofelt, your logic is correct, unfortunately you got the numbers mixed up - we have 60 labors after 10 days, not 26, but that's no big deal - once you get the logic, you can always re-check the numbers, so I guess your answer is correct too

 

[Multipack]

I answered your question correctly. Believe me lol. It's simple. Perhaps you didn't word it correctly...

 

[Lumia925]

I answered your question correctly. Believe me lol. It's simple. Perhaps you didn't word it correctly...

The question's exactly as her teacher wrote it, perhaps the teacher didn't use proper language then, or perhaps she copied it wrong, but as I understand, the question's like 50 labors can be fed for 16 days, these 50 start consuming the food, then after 10 days, another 10 labors join in. now we have 60 labors to feed, and the food remaining is whatever's left after the original 50 men ate for the first 10 days. We need to calculate how long the remaining food will last for 60 labors, and then add it to 10 to find out how long the food lasted in total.

Strangely enough, her teacher mentions the answer after each question- she just needs to show how to arrive at that answer - things weren't like this in my school days, we didn't have the answers pre-mentioned for our maths homework..

The answer mentioned is [strike]5[/strike] 15, and the logic used by Air Force to arrive to that answer makes perfect sense to me, so I guess I picked the correct best answer..

 

[Multipack]

You added 20% extra laborers, so that leaves 80% of 6 days left by my reasoning. Which is 4.8 days.

How can it last for 15 days when there's only 6 days left? lol

(Just realised it's how long in total.. so yeah one day less)

 

[Lumia925]

You added 20% extra laborers, so that leaves 80% of 6 days left by my reasoning. Which is 4.8 days.

How can it last for 15 days when there's only 6 days left? lol

(Just realised it's how long in total.. so yeah one day less)

Your reasoning appears incorrect to me because of this:- you're calculating 80% of 6 days, while you should be calculating [(80)*(quantity of food remaining after 50 people have consumed for 10 days)]/100.

Hope this makes sense. You're calculating a percentage on the number of remaining days, while you should be calculating a percentage on the quantity of food remaining.

 

[TMTOWTSAC]

I'm with ko888 on this one, it's an ambiguous question. When they ask "How long will the food last?" they are expressing a measurement of time, current tense. For that you need a starting point. They state, "After 10 days, 10 more labors join the company." Which means within the context of this question, 10 days have now passed, so you begin counting 10 days in, leaving 5 days of food remaining. By saying the answer is actually 15, they are counting from before the "after" so it's grammatically wrong for that answer. For 15, they should have said something like, "How many days in total did their food supply last?"

It's that Singapore logic problem all over again:

https://en.wikipedia.org/wiki/Cheryl's_Birthday

Which the test makers also got wrong btw.

Edit: Fixed link.

 

[Lumia925]

I'm with ko888 on this one, it's an ambiguous question. When they ask "How long will the food last?" they are expressing a measurement of time, current tense. For that you need a starting point. They state, "After 10 days, 10 more labors join the company." Which means within the context of this question, 10 days have now passed, so you begin counting 10 days in, leaving 5 days of food remaining. By saying the answer is actually 15, they are counting from before the "after" so it's grammatically wrong for that answer. For 15, they should have said something like, "How many days in total did their food supply last?"

It's that Singapore logic problem all over again:

https://en.wikipedia.org/wiki/Cheryl's_Birthday

Which the test makers also got wrong btw.

I see your point, and I agree with the language ambiguity observation you people made

 

[USAFRet]

This isn't rocket science, folks.

The actual answer to "How long will the food last?" is approx 4 months.

How, you might ask?
You forgot the variable of the human condition.

At the 10 day point, 10 new people are introduced
The original 50 are up in arms, and slay these upstart newcomers.
Returning the remaining food to 6 days left.
The next day, the 50 start to realize that no one is coming to save them.
Now that they have crossed the 'killing' portion, the 25 largest slay the other 25.

At this point we have 250 food units, and only 25 people.
So, food for another 10 days.

Wash, rinse, repeat...
Before long, we get down to 1 person, with 100+ food units left.
He lasts until summer.
Longer, if he slices off a bit of thigh meat to supplement his remaining "food units"

 

[TMTOWTSAC]

This isn't rocket science, folks.

The actual answer to "How long will the food last?" is approx 4 months.

How, you might ask?
You forgot the variable of the human condition.

At the 10 day point, 10 new people are introduced
The original 50 are up in arms, and slay these upstart newcomers.
Returning the remaining food to 6 days left.
The next day, the 50 start to realize that no one is coming to save them.
Now that they have crossed the 'killing' portion, the 25 largest slay the other 25.

At this point we have 250 food units, and only 25 people.
So, food for another 10 days.

Wash, rinse, repeat...
Before long, we get down to 1 person, with 100+ food units left.
He lasts until summer.
Longer, if he slices off a bit of thigh meat to supplement his remaining "food units"

Well, if you include the human condition, you'd need to account for delirium brought on by starvation and vitamin deficiency. At some point, when they're desperate enough, someone will be willing to order in from Domino's.