Question

Divide the number 520 into two parts in the ratio 5:8.
The parts of the number are ? and ?

Answer 1

200 and 320

Explanation:

Answer 2

The parts of the number are 200 and 320

Explanation:

System of Equations

Suppose a and b are the two parts. They must meet two conditions:

`a+b=520\qquad\qquad [1]`

`\displaystyle (a)/(b)=(5)/(8)\qquad\qquad [2]`

From [1], we have:

`b=520-a`

Replacing in [2]:

`\displaystyle (a)/(520-a)=(5)/(8)`

Cross-multiplying:

`8a=5*(520-a)`

Operating:

`8a=2600-5a`

Joining like terms:

`13a=2600`

Solving:

`a=2600/13=200`

a=200

Since:

`b=520-a\Rightarrow b=520-200`

b=320

The parts of the number are 200 and 320