Help With This Math Problem?

Question

A laundry company is selling a liquid and powder version of their soap. They did a survey and 5/7 said they used liquid, 1/3 said they dont use powder, 183 said they use both, and 20% said they use neither. How many people were surveyed?

Answer 1

I'm late for work so I will get you started.

L will equal the number of liquid only
P will equal the number of powder only
B will equal the number of both
N will equal the number of neither
T is the total number surveyed

B is given as 183
T = L + P + N + 183

5/7 said they used liquid. This includes L and B therefore

5/7 = (L + 183) / T

1/3 said they don't use powder. This includes L and N therefore

1/3 = (L + N) / T

20% said they use neither. Therefore

20% = 1/5 = N / T

Now you have 4 equations in 4 unknowns.

Hope this helps.

Answer 2

This Is A Set Question,
If You Draw A Venn Diagram, You'll Understand It Easily.

Assume:
The Number Of People Surveyed Is x
Set L is For Liquid Users
Set P is For Powder Users


Therefore;
N(L) = (5/7) x
N(P') = (1/3) x => N(P) = (2/3) x
N(LnP) = 183
N((LuP)') = (1/5)x => N(LuP) = (4/5) x

Thus,
N(LuP) = N(L) + N(P) - N(LnP)
4x/5 = 5x/7 + 2x/3 - 183
4x/5 = (15x+14x)/21 - 183
4x/5 = 29x/21 - 183

Multiply The Entire String By 105:

84x = 145x - 19215
61x = 19215
x = 315

Answer 3

we know that the percent have to add up to 100

this question uses a lot of logic
1. neither includes those who don't use powder with some extras
2. some of the people who don't use powder DO use liquid
3. those who use both can be included in liquid
5/7 = 71.4%
1/3 = 33.3%

there is a 13.3% who may use liqiud but do not use powder
this means that there are about 4.76% that use only liquid leaving 66.64% that use both

solve this by proportion
66.64/100 = 183/x
66.64x = 18300
x = 274.6

this means about 275 people were surveyed

hope this helps
(the guesser was only off by about 37...hehe)

Answer 4

L P f
0 0 =0.2N
0 1
1 0 =5N/7 - 183
1 1 183
N/5 + 5N/7 - 183 = N/3
21N + 75N - 19,215 = 35N
61N = 19,215
N = 315

Answer 5

I'm gonna throw out a random number....ill say about 312