The units digit of a two-digit number is 1 more than 4 times the tens digit. If the digits are reversed, the new number is 5 more than 3 times the original number. What is the number with the digits reversed?1 pointA. 15B. 29C. 51D. 92
Question
The units digit of a two-digit number is 1 more than 4 times the tens digit. If the digits are reversed, the new number is 5 more than 3 times the original number. What is the number with the digits reversed?1 pointA. 15B. 29C. 51D. 92
Solution
Let's solve this step by step:
Step 1: Let's denote the tens digit as x and the units digit as y. According to the problem, we have two equations:
y = 4x + 1 (since the units digit is 1 more than 4 times the tens digit)
10y + x = 3(10x + y) + 5 (since if the digits are reversed, the new number is 5 more than 3 times the original number)
Step 2: Simplify the second equation:
10y + x = 30x + 3y + 5
7y = 29x + 5
Step 3: Substitute y from the first equation into the second equation:
7(4x + 1) = 29x + 5
28x + 7 = 29x + 5
x = 2
Step 4: Substitute x = 2 into the first equation to find y:
y = 4*2 + 1 = 9
So, the original number is 29 and the number with the digits reversed is 92. Therefore, the answer is D. 92.
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