Volume and ratios

Question

Danny poured 78 liters of water into containers x,y, and z.The ratio of the volume of water in container x to the volume in container y is 5;2. The ratio of the volume of water in container y to the volume of water in container z is 8;11.

How much water was poured into container x?

How much more water was poured into container x than container z?

Answer 1

Since x and y are in the ratio 5 to 2,  x = 5a and y = 2a, for some positive number, a.

 

Since y and z are in the ratio 8 to 11, y = 8b and z = 11b, for some positive number, b.

 

So, since y = 2a and y = 8b, 2a = 8b.  Therefore, a = 4b.

 

We then have x = 5a = 5(4b) = 20b

                    y = 8b

                    z = 11b

 

We know that x+y+z =78

 

So, 20b + 8b + 11b = 78

 

                      39b = 78

 

                         b = 2

 

Thus, x = 20b = 40 liters

        

         y = 8b = 16 liters

 

         z = 11b = 22 liters

                 

 

Answer 2

x : y :: 5 : 2, y : z :: 8 : 11

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

x : y : z :: 20 : 8 : 11

 

x got 40

y got 16

z got 22