Answer:
The parts of the number are 200 and 320
Step-by-step explanation:
System of Equations
Suppose a and b are the two parts. They must meet two conditions:
[tex]a+b=520\qquad\qquad [1][/tex]
[tex]\displaystyle \frac{a}{b}=\frac{5}{8}\qquad\qquad [2][/tex]
From [1], we have:
[tex]b=520-a[/tex]
Replacing in [2]:
[tex]\displaystyle \frac{a}{520-a}=\frac{5}{8}[/tex]
Cross-multiplying:
[tex]8a=5*(520-a)[/tex]
Operating:
[tex]8a=2600-5a[/tex]
Joining like terms:
[tex]13a=2600[/tex]
Solving:
[tex]a=2600/13=200[/tex]
a=200
Since:
[tex]b=520-a\Rightarrow b=520-200[/tex]
b=320
The parts of the number are 200 and 320
