Step 1. Using the first two balances, we can form two equations that will help us to solve the problem.
Let x represent the cubes, y represent the spheres, and z represent the cylinders.
Then, the two equations are:
[tex]\begin{gathered} 3x+y=z+2y \\ 3x=5y \end{gathered}[/tex]
Step 2. We can simplify the first equation by substituting the second equation into it:
[tex]\begin{gathered} 3x+y=z+2y \\ since\text{ }3x=5y \\ 5y+y=z+2y \end{gathered}[/tex]
And now we simplify the operations between like terms in this last equation:
[tex]\begin{gathered} 6y=z+2y \\ 6y-2y=z \\ 4y=z \end{gathered}[/tex]
Step 3. So far, we have two equations that relate the x, y, and z values:
[tex]\begin{gathered} \boxed{3x=5y} \\ \boxed{4y=z} \end{gathered}[/tex]
Step 4. In question #3 we are given a value for the sphere (remember that for us the sphere is y), and that value is 9 pounds:
[tex]y=9[/tex]
To find the weight of the cube and the cylinder (x and z) we substitute the given value of y into our two equations from step 3:
[tex]\begin{gathered} 3x=5(9) \\ 4(9)=z \end{gathered}[/tex]
Solving the first equation for x and the second for z:
[tex]\begin{gathered} 3x=45\rightarrow x=45/3\rightarrow\boxed{x=15} \\ \boxed{36=z} \end{gathered}[/tex]
The cube weighs 15 pounds and the cylinder weighs 36 pounds.
Answer: 15 and 36
