Question 1012691
you are given that:


x:y:z = 5:7:3


y = z+56


y:z = 7:3 is the same as y/z = 7/3.


since y has 56 more marbles than z, then you get y = z+56.


replace y with z+56 in the formula of y/z = 7/3 to get (z+56)/z = 7/3


multiply both sides of the equation by z to get z+56 = 7z/3


multiply both sides of the equation by 3 to get 3*(z+56) = 7z


distribute the multiplication to get 3z + 168 = 7z


subtract 3z from both sides of the equation to get 168 = 4z


divide both sides of the equation by 4 to get z = 42


since y is 56 more than z, then y = 98


since the ratio of x:y = 5:7 is the same as x/y = 5/7, you get:


x/y = 5/7


since y = 98, the equation becomes x/98 = 5/7


multiply both sides of the equation by 98 to get x = 5 * 98/7


solve for x to get x = 70.


your solution is that x = 70, y = 98, and z = 42.


y is 56 more than z because 42 + 56 = 98.


ratio of x to y is 5/7 because 70/98 = 5/7.


ratio of y to z is 7/3 because 98/42 =  7/3.