1) The average number of patrons in cinemas I,II, III & IV is 350. There are 775 patrons in cinemas 1 & II. If

Question

there are 69 more patrons in cinema III than in cinema IV, how many patrons are there in cinema III ?

2) The average mass of Ravi, Sanur & Tarman is 37 kg. Ravi & Sanur together have an average mass of 34kg while Sanur & Tarman together have an average mass of 35kg. What is the average mass of Ravi & Tarman ?

Answer 1

1)
ok I will use A ,B ,C, & D for the number of patrons in cinema I,II ,III , IV
so the average = the sum of patrons / number cinemas
(A + B + C + D) / 4 = 350
A+ B + C + D = 4 * 350
A+ B + C + D = 1400
where A + B = 775
775 + C + D = 1400
where D = C - 69
So
775 + C + C - 69 = 1400
2C + 706 = 1400
2C = 1400 - 706
2C = 694
C = 694 / 2
C = 347 Patrons

so there is 347 patrons in cinema III









2)
tlet's use the first letter for every one ..R , S & T
so
the average = sum of weights / number of ppl we have
(R + S + T ) / 3 = 37
R + S +T = 3 * 37
R + S + T = 111

R + S = 2 * 34
R + S = 68 Kg
R + S + T = 111
T = 111 - 68 = 43 Kg

S + T = 2 * 35
S + T = 70 Kg
R + S + T = 111
R = 111 - 70 = 41 Kg



then
average of R & T
(R + T) / 2 = (41 + 43 ) / 2
= 84 / 2
= 42 Kg

Answer 2

I=a, II=b, III=c, and IV=d
(a+b+c+d)/4=350
a+b+c+d=350*4=1400
a+b=775 subtract from the above equation
c+d=625
c=d+69 substituting into the above equation
(d+69)+d=625
2d+69=625
2d=556
d=278
c=278+69=347 in cinema III


2) (R+S+T)/3=37
R+S+T=37*3=111
(R+S)/2=34
R+S=68 subtracting from line 2
T=111-68=43
(S+T)/2=35
S+T=35*2=70 we know that T=43
S+43=70
S=27 substituting back into the line 2
R+27+43=111
R=41
then (R+T)/2=(41+43)/2=42
Average mass of Ravi and Tarman is 42kg

Answer 3

You might want to use Venn Diagrams to help you visualize this.

1. If the average number is 350, this means there are 1400 in ALL four cinemas. We know how many are in I and II, so we can compute the total number in III and IV. Call that total T34. If the number in cimema IV is N4, the number in cinema 3 is N4+69. So N4+N4+69= T34. Follow it through.

2. RST total mass = 3*37 = 111.
If R&S ave mass is 34, their total is 68. The rest is Tarman's (43)
In a like manner, if S&T ave mass is 35, their total is 70. We know Tarman's is 43, so Sanur must be 27.
Since Sanur's is 27, Ravi's must be 41.
Now we can find thee average mass of Ravi and Tarman.

Answer 4

Cinema 1 = a, Cinema 1 = b, Cinema 1 = c, Cinema 1 = d
(a+b+c+d)/4=350
a+b = 775
c = d + 69
(775 + c + [c + 69] )/ 4 = 350
(775 + c + [c + 69] ) = 1400
844 + 2c = 1400
2c = 556
c = 278

( r + s + t ) / 3 = 37
( r + s ) / 2 = 34
( s + t ) / 2 = 35
( r + t ) / 2 = ? <--Find

( r + s ) / 2 = 34
r+s = 78
r = 78 - s
( s + t ) / 2 = 35
( s + t ) = 70
t = 70 - s
( r + s + t ) / 3 = 37
( [78-s] + s + [70-s] ) / 3 ) = 37
78 - s + s + 70 - s = 111
156 - s = 111
-s = -45
s = 45
( s + t ) / 2 = 35
( 45 + t ) / 2 = 35
45 + t = 70
t = 25
( r + s ) / 2 = 34
r + 45 = 78
r = 33
( r + t ) / 2 = ?
(33 + 25) / 2 = 58/2 = 29 <--Answer

Answer 5

1. 347
2. 36

Answer 6

1) 243
2) IDK!