SOLUTION: Hi box x box y box z contain marbles in the ratio of 5:7:3.If there are 56 more marbles in box y than box z, how many marbles in all 3 boxes thanks

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Question 1012691: Hi
box x box y box z contain marbles in the ratio of 5:7:3.If there are 56 more marbles in box y than box z, how many marbles in all 3 boxes
thanks
Found 2 solutions by Edwin McCravy, Theo:
Answer by Edwin McCravy(20065)   (Show Source): You can put this solution on YOUR website!
Use the principle:

If x:y:z = a:b:c

then

, , .

We are given x:y:z = 5:7:3, then

, , 

or

, , 

Reducing and letting the sum x+y+z = s, the sum of the marbles
in the box,

, ,

there are 56 more marbles in box y than box z
y = z+56



Cross multiply:



Solve by substitution.  The answer is what you get for s.

Edwin
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
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.


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