Math Related Help Needed

[Boomwebsearch]

Imagine the following situation and please let me know what the solution is to this problem and some explanation about how you solved this.

 

The walls of a square room need painting. Each of the four walls is 12ft wide by 8.5 feet tall. One gallon of paint covers 75ft^2  (75 feet squared). How many gallons of paint will you need?

[79wjd]

Find the area of all four walls and divide it by the amount of paint area in a gallon of paint. 

 

Walls are 12x8.5, and there are four of them. 

1 Gallon of paint covers 75 square feet. 

[Eduard the weeb]

yeah I just cheat and use one of those photo math things for home because I am to lazy to due math at school and home.

[Boomwebsearch]

1 hour ago, djdwosk97 said:

Find the area of all four walls and divide it by the amount of paint area in a gallon of paint. 

 

Walls are 12x8.5, and there are four of them. 

1 Gallon of paint covers 75 square feet. 

Would the solution be 5.44 gallons   ?

[79wjd]

Just now, Boomwebsearch said:

Would the solution be 5.44 gallons   ?

Yes, but you probably can't buy part of a gallon, so 6 gallons (unless you can, then 5.44).

[Boomwebsearch]

1 hour ago, djdwosk97 said:

Yes, but you probably can't buy part of a gallon, so 6 gallons. 

OK, thanks so much for your help!

[Dash Lambda]

I mean, if it's a square room then the walls don't have an area so...

Actually, I wonder if the concept of a "room" has an analogue for 2D, or if it's even dependent on dimensions...

[Mug]

So glad we use the metric system for things like this.

[RyomaSJibenG]

2 hours ago, Dash Lambda said:

I mean, if it's a square room then the walls don't have an area so...

Actually, I wonder if the concept of a "room" has an analogue for 2D, or if it's even dependent on dimensions...

well in the case of 2D games, when we enter a room, the only difference it makes from outside and inside is none other than the wall in background, maybe some lighting, but just the background wall

[79wjd]

2 hours ago, Mug said:

So glad we use the metric system for things like this.

Yeah, 3.6576 and 2.5908 meters is a lot easier to work with than 12 and 8.5 feet. 

[RyomaSJibenG]

1 hour ago, djdwosk97 said:

Yeah, 3.6576 and 2.5908 meters is a lot easier to work with than 12 and 8.5 feet. 

Yeah, 13.1234 and 1.4829feet is  lot easier to work with than 4 and 3 meters

[79wjd]

3 minutes ago, RyomaSJibenG said:

Yeah, 13.1234 and 1.4829feet is  lot easier to work with than 4 and 3 meters

i'm not the one who decided to make the stupid comment about the metric system being better. But regardless of that, there obviously is no one system that eliminates the need for fractions of a unit, however, rounding has a much smaller impact on feet than it does on meters.

 

Doing mental math on quarters/halves is easy, so 13*1.5 = 19.5 compared to the actual result of 19.46, that's a relative error of (|19.5-19.460689|)/19.460689=0.2%.

Alternatively 3.6576*2.5908 -> 3.5*2.5=8.75 compared to the actual result of (|8.75-9.47611008|)/9.47611008=7.66%

[Dash Lambda]

13 minutes ago, djdwosk97 said:

-snip-

Mental arithmetic is not justifiably easier or harder or more or less accurate with either of the units, they're just different lengths. Feet are probably more fitting for a lot of day-to-day measurements just because of the scale, but there is no difference in the calculations beyond scale.

That being said, the metric system is consistent, which is something the imperial system is directly opposed to being. I vastly prefer working with a uniform system than having to remember how many feet are in a mile, how many tablespoons are in a cup, how many ounces are in a pound, etc... When you need to do more than shift a decimal place to convert units within the same system, you need a new system.

[79wjd]

36 minutes ago, Dash Lambda said:

Mental arithmetic is not justifiably easier or harder or more or less accurate with either of the units, they're just different lengths. Feet are probably more fitting for a lot of day-to-day measurements just because of the scale, but there is no difference in the calculations beyond scale.

No doubt the metric system is nicer to work with, but smaller units, as you said, are more useful for day-to-day use. Take Fahrenheit vs. Celsius -- on a short timescale (read: days) the temperature generally fluctuates a small amount, so Fahrenheit gives you a better scale for measuring daily temperatures. It's like the whole mm/dd vs. dd/mm argument -- which is more important to know on a day-to-day basis? The days since they change 30~ times (daily) compared to the months which change 12 times, so unless you're going in and out of a comma, dd/mm does make more sense. 

 

Mental arithmetic is the same if you round to an easy to work with number, but the error from rounding is much larger when you're using larger units, so your estimation will be more accurate when using the (smaller) imperial scale.

36 minutes ago, Dash Lambda said:

That being said, the metric system is consistent, which is something the imperial system is directly opposed to being. I vastly prefer working with a uniform system than having to remember how many feet are in a mile, how many tablespoons are in a cup, how many ounces are in a pound, etc... When you need to do more than shift a decimal place to convert units within the same system, you need a new system.

Mile = 5280 feet

Pound = 16oz

Cup = 8oz = 16tbsp

1 tbsp = 3 tsp

 

Again, a consistent system would no question be nice, but smaller units is one thing that I think is a big advantage to the imperial system for day-to-day use.

[Mug]

14 hours ago, djdwosk97 said:

Mental arithmetic is the same if you round to an easy to work with number, but the error from rounding is much larger when you're using larger units, so your estimation will be more accurate when using the (smaller) imperial scale.

Mile = 5280 feet

Pound = 16oz

Cup = 8oz = 16tbsp

1 tbsp = 3 tsp

 

smaller units is one thing that I think is a big advantage to the imperial system for day-to-day use.

For me, I only need to remember tens whereas you have to work out eighths, sixteenths, thirds etc. Imperial isn't smaller, we use centimetres for small distances, which is conveniently convertible by factors of 10 to larger measurements (ie: dm, m, km). Not to mention the silly units of measurement that can be used in imperial; a pole, a perch, a rod. I mean I'm sure someone could do it but it's just not as convenient or efficient to divide by anything other than 10 if you don't need to.

 

There is no argument in this, the metric system is better. What makes even less sense than this argument taking place is that we (in the UK) sometimes use both systems. Miles for distance but metres for measuring lengths, feet and stones for people's height and weight, and litres for buying fuel at the pumps but mpg for fuel economy. But then again, we take little pride in preserving antiquated units of measurement to make our country feel more important or nostalgic.

 

All aside, I think it's incredibly important to use metric on a daily basis, if anything for children to understand science better. When using quantities like molar in Chemistry, it gives students a greater understanding when they're using units that they use every day (litres, grams etc) as it's more relevant to them. How is a budding particle physicist meant to understand what a femtometre is? Oh, well duh, it's 9.144x10¹⁴ feet, of course.

 

15 hours ago, djdwosk97 said:

i'm not the one who decided to make the stupid comment about the metric system being better

I'm not the one that got offended by - and took the time out of their (I'm sure) incredibly busy day to reply to - a 'stupid comment about the metric system being better'.

[79wjd]

19 minutes ago, Mug said:

For me, I only need to remember tens whereas you have to work out eighths, sixteenths, thirds etc. Imperial isn't smaller, we use centimetres for small distances, which is conveniently convertible by factors of 10 to larger measurements (ie: dm, m, km). Not to mention the silly units of measurement that can be used in imperial; a pole, a perch, a rod. I mean I'm sure someone could do it but it's just not as convenient or efficient to divide by anything other than 10 if you don't need to.

Everything I said above still applies regardless of whether you choose to work in centimeters or meters. You're still going to be rounding, and the rounding error will still be larger in the metric system. Of course decimeters are a thing (which would yield a much more accurate .6% error in the example), but they're not really used and there also a bit too small making intermediate numbers harder to work with, although the imperial system has that same problem with even larger numbers since there isn't really anything between feet and miles.

Quote

Doing mental math on quarters/halves is easy, so 13*1.5 = 19.5 compared to the actual result of 19.46, that's a relative error of (|19.5-19.460689|)/19.460689=0.2%.

Alternatively 3.6576*2.5908 -> 3.5*2.5=8.75 compared to the actual result of (|8.75-9.47611008|)/9.47611008=7.66%

Also, you only have to work with inches, feet, and miles -- no one uses poles, perches, or rods; and for the most part, you're not sitting there converting between the three because there usually isn't much of a reason to do any conversions. Generally the given unit is the useful unit you want to end up with anyway. 

 

 

For science, the metric system is no question better, but you're also not doing a lot of mental math in science as precision is important; the area of a room or other day-to-day math is not important enough to require extreme accuracy and thus rounding is commonplace. 

 

Oh, and if this 'budding scientist' needs a lot of exposure to be able to figure out the metric system, then I'm sorry to say, he isn't going to grow up to be much of a scientist. 

[Dash Lambda]

4 hours ago, djdwosk97 said:

-snip-

You know, generally things that would be measured in meters in metric are measured in yards in imperial. The more direct comparison, in terms of usage, would be feet to centimeters -Which makes metric a lot more precise, but also a lot more clunky to say.

What I believe is that we should use the imperial system colloquially where appropriate, 'cause a lot of the time it really does fit better into day-to-day stuff and conversational speech, but in any even remotely formal context we should only use metric.

[79wjd]

10 minutes ago, Dash Lambda said:

You know, generally things that would be measured in meters in metric are measured in yards in imperial.

No one actually uses yards for anything other than football.

Quote

The more direct comparison, in terms of usage, would be feet to centimeters -Which makes metric a lot more precise, but also a lot more clunky to say.

What I believe is that we should use the imperial system colloquially where appropriate, 'cause a lot of the time it really does fit better into day-to-day stuff and conversational speech, but in any even remotely formal context we should only use metric.

No argument there. 

[Boomwebsearch]

24 minutes ago, djdwosk97 said:

No one actually uses yards for anything other than football.

No argument there. 

The term of "yards" could be used for applications such as referring to a yardstick, finding the distance of something such as a room, etc. Although it is less commonly used when compared to other mathematics terms.

[Chaos_Sorcerer]

≈ 20.6 L

[Levisallanon]

edit: nevermind I read something wrong.