The length of segment AB is 30 cm. Point C divides segment AB into segments AC and CB, and 25%

| May 26, 2021 | education

The length of segment AB is 30 cm. Point C divides segment AB into segments AC and CB, and 25% of the length of segment AC is equal to 1/6 of the length of segment CB. Find the length of the line segment AC.

Let us introduce the notation. Let the segment AC be equal to x, then the segment BC will be equal to (30 – x), since the entire segment AB is equal to 30 cm.

Let’s convert the percentage to a decimal fraction: 25% = 0.25.

Let us express 25% of the length of the segment AC: 0.25 * x.

Let us express 1/6 of the length of the CB segment: 1/6 * (30 – x).

The equation turns out: 0.25 * x = 1/6 (30 – x).

Since 0.25 = 1/4, we get the equation:

1 / 4x = 5 – 1 / 6x;

1 / 4x + 1 / 6x = 5;

3 / 12x + 2 / 12x = 5;

5 / 12x = 5;

x = 5: 5/12 = 5 * 12/5 = 12 (cm) – AC segment.

Answer: the length of the AC segment is 12 cm.



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