### Math Notes

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#### Algebra Solutions

##### Topics || Problems

A line 20 inches long is divided into two parts whose lengths have the ratio 3:7. Find the lengths of the parts.

Solution:

Let $$x$$ be the first part and $$y$$ be the second part.

$$x + y = 20$$

The ratio is 3:7, thus $$3:7 = x:y$$

$$\frac{3}{7} = \frac{x}{y}$$

$$x = \frac{3y}{7}$$

$$\frac{3y}{7} + y = 20$$

$$\frac{10y}{7}=20$$

$$y = 14$$

$$x = 20-14 = 6$$

Thus, the length of the shorter part is 6 inches and the longer part is 14 inches.