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# Ratio problem - Solve ASAP NEED SERIOUS HELP

2 questions:

a) - Danny poured 78 liters of water into containers x,y,z. The ratio of the volume of water in container X to the volume of water in container Y is 5:2. The Ratio of the volume of water In Y to the volume in Z is 8:11

a- How much water was poured into container X
b - How much more water was poured into container x than z

b) - Lara has three cats: Socks, Princess, and Luna. The ratio of Sock's weight to Princess's weight is 4:5. The ratio of Princess's Weight to Luna's weight is 6:7. What is the ratio of Sock's weight to Luna's weight.

No algebra and go into as much detail as possible. Thanks

X+ Y + Z = 78

X/Y = 5/2         Solving  System of equation, by method is called back substitution.

Y/Z = 8/11

Y = 2X/ 5

Z = 11Y/ 8Z = 11* 2/5 X / 8 = 11X/20

X + 2X/5 + 11X/20 = 78(20)                  / substitution of Y. Z for X

20X +8X + 11X = 78( 20)

39 X = 78(20)

X = 40 Liter

Y = 2/5(40) = 16 Liter

c)    Z =  11/20 X = 11/20 * 40 = 22

Next problem is the same

S - Sock's Weight
P - Princess Weight
L - Luna's weight

S/ P = 4/5
P/L = 6/7
S/ L = ?

S/L = S/P * P/ L = 4/5* 6/7 = 24/35

(1)  ...  x : y = 5 : 2

(2)  ...  y : z = 8 : 11

Let's rewrite (1) as

x : y = 20 : 8 , and
y : z = 8 : 11

Now, both ratios we can rewrite as one:

x : y : z = 20 : 8 : 11

20 + 8 + 11 = 39 units

Three containers contain 78 liters and that is 39 units, let's find how many litters in 1 unit.

78 / 39 = 2 litters per unit

(a) Container "x" contains 20 * 2 = 40 litters
Container "y" contains   8 * 2 = 16 litters
Container "z" contains 11 * 2 = 22 litters
--------------
78 litters

(b)  40 - 22 = 18 litters more in "x" than in "z"

==========
Sock's weight to Princess's weight is 4:5. The ratio of Princess's Weight to Luna's weight is 6:7.
Let Sock's weight be "wS" , Princess's weight be "wP" and Luna's weight be "wL"
wS : wP = 4 : 5
wP : wL = 6 : 7

Least common multiple of 5 and 6 is 30, then, let's multiply first ratio by 6 and second ratio by 5

wS : wP = 24 : 30
wP : wL = 30 : 35

wS : wP : wL = 24 : 30 : 35 ---->

wS : wL = 24 : 35  = 24 / 35