# Equation1

Algebra

### Equation1

Find each:

The sum of two numbers is s; m times their sums is equal to n times their difference.

a and c = the numbers.

a + c = s

a + c = ms = a - c = n

Not sure how to continue.
Guest

### Re: Equation1

$$\begin{array}{|l}a+c=s\\m(a+c)=n(a-c)\end{array}$$

$$\begin{array}{|l}c=s-a\\ms=n(a-(s-a))=n(2a-s)\end{array}$$

$$2a-s=\frac{ms}{n}$$

$$2a=s+\frac{ms}{n}=\frac{m+n}{n}\cdot s$$

$$a=\frac{m+n}{2n}\cdot s$$

$$c=s-a=\left(1-\frac{m+n}{2n}\right)\cdot s=\frac{n-m}{2n}\cdot s$$

Verification:

$$a+c=\left(\frac{m+n}{2n}+\frac{n-m}{2n}\right)\cdot s=\frac{2n}{2n}\cdot s=s$$

$$m(a+c)-n(a-c)=m.s-\cancel{n}\cdot\frac{\cancel{2}m}{\cancel{2}\cancel{n}}\cdot s=m.s-m.s=0$$

$$\Rightarrow m(a+c)=n(a-c)$$

Answer: $$a=\frac{m+n}{2n}\cdot s;\ c=\frac{n-m}{2n}\cdot s$$
Guest

Thanks.
Guest