Question

Make 450 the second part equal to the sixth fifth of the first part and the third part equal to the fifth fourth of the second part.

Answer 1

Answer:

You can create three equations from the information in the question. This first equation is simply the first phrase in the sentence:

a+b+c=243

From the other information about the equality of the proportions of the parts, you can derive two more equations:

a2−b3=0

b3−c4=0

This gives three linear equations, which could be enough to solve the problem. If we pose it as a matrix equation, we have:

⎛⎝⎜⎜11201−131310−14⎞⎠⎟⎟⎛⎝⎜abc⎞⎠⎟=⎛⎝⎜24300⎞⎠⎟

The determinant of this matrix is not zero, indicating we can solve this problem. If you don’t know what a determinant is, don’t worry about it. You can solve this matrix equation using Gaussian elimination or using some computational environment, like Matlab. The solution is

a=54

b=81

c=108