Question

if m men can paint a house in d days, how many days will it take m+2 men to paint the same house?

Answer 1

\[A) D+2\]
\[B) D-2\]
\[C) \frac{ M+2 }{ MD }\]
\[D) \frac{ MD }{ M+2 }\]
\[E) \frac{ MD+2D}{M }\]

Answer 2

So you have to make a ratio between the amount of men and the amount of days spent, can you do that?

Answer 3

uhhh m:d
and m+2:d+2 ?

Answer 4

Nope, sorry not that simple you have We don't know big D so pretend there is a divided sign over the m and m+2 and d and D
m = d
m+2 = D

Answer 5

Then you have to solve for D

Answer 6

how you do that id d=m+2?

Answer 7

unless you mean substitute m for d?
so d+2=D ?

Answer 8

You have a ratio of m : m+2
and you are trying to find how much D is in terms of d.
which is not always the same ratio.

So you have to make an equation out of it and solve for a unknown. D

Answer 9

The equation I made was m/(m+2) = d/D

Then you just have to solve for D

Answer 10

then i got \[(D)\frac{ m }{ m+2 }=\frac{ d }{ D }(D)\]
then \[(D)\frac{ m+2 }{ m}=d\]
now what?

Answer 11

umm i meant \[(D)\frac{ M}{m+c }=d\]

Answer 12

Now you multiply by m+2 and divide by m.

Answer 13

so like
\[D=\frac{ d(m+c) }{ m }\rightarrow D=\frac{ dm+dc }{ m } \]?

Answer 14

Yup! except the c is supposed to be a 2.

Answer 15

uhh replace c with 2
my retardedness happend

Answer 16

lol

Answer 17

We all do it :x

Answer 18

thank you!!!

Answer 19

Your welcome!

Answer 20

i got more question..wanna answer em? :3

Answer 21

I can go for one more. Then I gotta sleep.

Answer 22

thanks i owe you one....sorry for the crappy internet

there is enough food at a picnic to feed 20 adults or 32 children.If there are 15 adults at the picnic, how many children can still be fed?
A)6
B)8
C)12
D)16
E)18

Answer 23

So can you make the equation?

Answer 24

well i got
20a=32c
15a+xc

Answer 25

Remember in ratios you have to keep all of the a's and c's on one side of the equation while making it.

Answer 26

So you need to do
total adults / adults there = total children / children there

Answer 27

oh.... so like \[\frac{ 20 }{ 15 } = \frac{ 32 }{ x }\]

Answer 28

Yup, now you just solve for x :)

Answer 29

x=24 ?

Answer 30

Yup it does!

Answer 31

ok... so whats next?

Answer 32

Well x was the coefficient of your children there, so you can have 24 children with 15 adults there.

Answer 33

oh so like 24 children=15 adult so you can do 32-24=8
so you can have 8childrens?

Answer 34

Erm... Well no, but if 24 isn't the right answer, then I don't know what is because if you take the ratio of total children to total adults you get a ratio of 32/20 and that is 1.6 so if you multiply that by the 15 adults that are there then you get 24 also.

Just doing the same thing a different way and still getting the same answer... I really don't know. I'm sorry.

Answer 35

oh ok its ok :)

Answer 36

well good night :)

Answer 37

Good night

Answer 38

@ineedhelpnow08, your original question involves inverse proportions

Answer 39

\[\frac{MD + 2D}{M}\] is not the correct answer. I can demonstrate why.

Answer 40

Let's assume it takes 5 men 2 days to paint a house. How many days would it take 7 men to paint the house?

Answer 41

Let's set it up in a way similar to @Arfney's setup:

\[\frac{5 \space\text{men}}{7\space\text{men}} = \frac{2 \space\text{days}}{x \space\text{days}}\]

If we solve for x, then it should be less than 2 since we have more men working:

\[\frac{5}{7} = \frac{2}{x}\]
\[5x = 14\]
\[x = \frac{14}{5}\]
\[x \approx 2.8\]

This cannot be correct, because this would mean that with 7 men it would take longer to paint a house than with 5 men.

Answer 42

The correct approach is to understand that we're dealing with inverse proportions. We know it is inverse proportions because with MORE men, it should take LESS days. In other words, if the number of men INCREASE, then the number of days DECREASES.

So...how shall we proceed? By simply using the formula for inverse proportion:

xy = k

When we have inverse proportions, we are usually dealing with two separate cases. Such is true for this problem:

In the first case, x = m, y = d...so

md = k

In the second case,
x = m + 2, y = D, so:

(m + 2)(D) = k

So putting the two together we have:

md = k
(m + 2)(D) = k

and k is the constant of variation so it is the same for both cases therefore, set k = k:

k = k
md = (m + 2)(D)

Now, we can solve for D:

\[\frac{md}{m + 2} = D\]

Which is equivalent to one of your given answer choices.

To test to make sure it is correct, lets go back to the sample problem. We understand that it needs to take 7 men LESS than 2 days to paint the house, so lets input the numbers and see if our equation holds true:

m = 5
d = 2
m + 2 = 7

\[\frac{(5)(2)}{7} = \frac{10}{7} = \frac{7 + 3}{7} = \frac{7}{7} + \frac{3}{7} = 1 + \frac{3}{7} = 1 \frac{3}{7}\]

\(\large 1 \frac{3}{7} < 2\)

So we know our equation is correct :)

Answer 43

thanks..... but too late already hand in the homework :I

Answer 44

I know...I figured that may have happened. Sorry about that.