A two digit number is 4 times the sum of its two digits. The number that is…
2020
A two digit number is 4 times the sum of its two digits. The number that is formed by reversing its digits is 27 more than the original number. What is the number?
Answer: B. 36 — To find the two-digit number shown in image_8cd9fb.png, we can represent the number as 10x + y, where x is the tens digit and y is the units digit.…
- A.
27
- B.
36
- C.
42
- D.
54
Attempted by 5 students.
Show answer & explanation
Correct answer: B
To find the two-digit number shown in image_8cd9fb.png, we can represent the number as 10x + y, where x is the tens digit and y is the units digit.
Step-by-Step Calculation
Condition 1: The number is 4 times the sum of its digits.
10x + y = 4(x + y)
10x + y = 4x + 4y
6x = 3y, or y = 2x
Condition 2: The reversed number (10y + x) is 27 more than the original number.
(10y + x) - (10x + y) = 27
9y - 9x = 27
y - x = 3
Solve the system of equations:
Substitute y = 2x into the second equation: 2x - x = 3
x = 3
Find y: y = 2(3) = 6
The number is 10(3) + 6 = 36.