If the sum of the digits of a two-digit number is 9 and the number is 4 times th

If the sum of the digits of a two-digit number is 9 and the number is 4 times the sum of its digits, what is the number? (2021)

If the sum of the digits of a two-digit number is 9 and the number is 4 times the sum of its digits, what is the number? (2021)

Step 1: Let the two-digit number be represented as 10a + b, where 'a' is the tens digit and 'b' is the units digit.
Step 2: According to the problem, the sum of the digits (a + b) is equal to 9.
Step 3: The problem also states that the number (10a + b) is equal to 4 times the sum of its digits (4(a + b)).
Step 4: Substitute the sum of the digits into the equation: 10a + b = 4 * 9.
Step 5: Simplify the equation: 10a + b = 36.
Step 6: Now we have two equations: a + b = 9 and 10a + b = 36.
Step 7: From the first equation (a + b = 9), we can express b as b = 9 - a.
Step 8: Substitute b in the second equation: 10a + (9 - a) = 36.
Step 9: Simplify this equation: 10a + 9 - a = 36, which becomes 9a + 9 = 36.
Step 10: Subtract 9 from both sides: 9a = 27.
Step 11: Divide both sides by 9: a = 3.
Step 12: Now substitute a back into the equation for b: b = 9 - 3 = 6.
Step 13: The digits are a = 3 and b = 6, so the two-digit number is 10a + b = 10*3 + 6 = 36.

No concepts available.