The sum of the digits on a digital clock is 15. The number of minutes is 5 times the number of hours. Wheat time is it?
7:35
To solve this question, we need to find the time on the digital clock that satisfies the given conditions - the sum of the digits is 15 and the number of minutes is 5 times the number of hours.
Let's break down the problem step by step:
Step 1: Let's assume the digits on the digital clock are represented by two variables, A and B, for the hour and minute respectively. A will represent the tens digit, and B will represent the units digit.
Step 2: The sum of the digits is 15, so we can write the equation A + B = 15.
Step 3: The number of minutes is 5 times the number of hours. Since there are 60 minutes in an hour, we can also write the equation 60A + B = 5A.
Step 4: Now we have two equations with two variables:
Equation 1: A + B = 15
Equation 2: 60A + B = 5A
Step 5: We can solve this system of equations to find the values of A and B. Subtracting 5A from both sides of Equation 2, we get:
55A + B = 0
Step 6: Subtract Equation 1 from the modified Equation 2:
(55A + B) - (A + B) = 0 - 15
54A = -15
Step 7: Divide both sides of the equation by 54:
A = -15 / 54 = -5 / 18
Step 8: Since time cannot be negative, we know that A must be a positive integer. However, since -5 / 18 is not a positive integer, there is no valid solution for A and B that satisfies the given conditions.
Therefore, based on the given conditions, there is no valid time on the digital clock that matches the criteria of the sum of the digits being 15 and the number of minutes being 5 times the number of hours.