Point C is marked on the segment AB, the length of which is 62 cm. Find the lengths of the segments AC and CB, if 25% of the segment AC are equal to 4/15 of the segment CB.
The solution of the problem:
First, let’s define that 25% is 1/4.
Next, we form an identity using the condition of this problem: (1/4) AC = (4/15) CB.
To get rid of two unknowns, we represent CB as AB – AC, since AB is known.
Let’s rewrite the identity with changes and simplify as much as possible: (1/4) AC = (4/15) CB; (1/4) AC = (4/15) * (AB – AC); (1/4) AC = (4/15) * (62 – AC); AC / 4 = (248 – 4AC) / 15.
Using the proportion, we get: 15AC = 992 – 16AC; 31AC = 992; AC = 32.
CB = AB – AC = 62 – 32 = 30.
Answer: 30; 32.
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