Find three natural numbers about which it is known that the first is 2/3 of the second, the third is 30% of the first, and the difference between the second and the third is 96.
Let us denote the second number by x2.
Let us express the first and third numbers in terms of x2.
According to the condition of the problem, the first number is 2/3 of the second, therefore, the first number should be equal to 2×2 / 3.
Also, the problem statement says that the third number is 30% of the first, therefore, the third number should be equal to (30/100) * 2x^2 / 3 = (3/10) * 2x^2 / 3 = x^2 / 5.
By the condition of the problem, the difference between the second and third numbers is 96, therefore, we can draw up the following equation:
x^2 – x^2 / 5 = 96,
solving which, we get:
4x^2 / 5 = 96;
x^2 / 5 = 96/4;
x^2 / 5 = 24;
x^2 = 5 * 24 = 120.
Find the first and third numbers:
2x^2 / 3 = 2 * 120/3 = 2 * 40 = 80;
x^2 / 5 = 120/5 = 24.
Answer: 80, 120 and 24.
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