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Dviženklio skaičiaus skaitmenų suma lygi mažiausiam dviženkliam skaičiui, o dešimčių skaitmuo – keturis kartus mažesnis už vienetų skaitmenį. Raskite tą skaičių.

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Algebra 2right chevron icon
Csc, sec, and cot of special anglesright chevron icon

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Q. Dviženklio skaičiaus skaitmenų suma lygi mažiausiam dviženkliam skaičiui, o dešimčių skaitmuo – keturis kartus mažesnis už vienetų skaitmenį. Raskite tą skaičių.
  1. Define Digits: Let's denote the tens digit as 'aa' and the units digit as 'bb'. The two-digit number can be represented as 10a+b10a + b.
  2. Sum of Digits: The smallest two-digit number is 1010. So, the sum of the digits a+ba + b should equal 1010.
  3. Relation between Digits: It's given that the tens digit is four times smaller than the units digit, so we can write a=b4.a = \frac{b}{4}.
  4. Substitute and Simplify: Substitute the value of aa from the third step into the second step equation: b4+b=10\frac{b}{4} + b = 10.
  5. Solve for Units Digit: Combine like terms to solve for bb: (14)b+b=10(\frac{1}{4})b + b = 10, which simplifies to (54)b=10(\frac{5}{4})b = 10.
  6. Find Tens Digit: Multiply both sides by 45\frac{4}{5} to solve for bb: b=(10×45)b = (10 \times \frac{4}{5}), which simplifies to b=8b = 8.
  7. Form Two-Digit Number: Now, plug the value of bb back into the equation a=b4a = \frac{b}{4} to find aa: a=84a = \frac{8}{4}, which simplifies to a=2a = 2.
  8. Calculate Final Result: The two-digit number is formed by the tens digit 'aa' and the units digit 'bb', so the number is 10a+b=10×2+810a + b = 10\times2 + 8.
  9. Calculate Final Result: The two-digit number is formed by the tens digit 'aa' and the units digit 'bb', so the number is 10a+b=10×2+810a + b = 10\times2 + 8.Calculate the two-digit number: 10×2+8=20+810\times2 + 8 = 20 + 8, which equals 2828.

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