Could you please explain the quickest way to calculate these questions?
1)Julian's age has the same figures as his dad's with the digits reversed. The sum of their ages is 77 and Julian is 27 years younger than his dad. How old is Julian?
I used some basic logic
What 2-digit number and that number reversed add up to 77 ?
16 and 61
25 and 52
34 and 43
Which of these look like logical numbers for father/son ages, and have a difference of 27 ??
You asked for the quickest way.
To find Julian's age, we need to follow these steps:
1) Let's assume Julian's age is represented by the digits "AB" (where A represents the tens digit, and B represents the ones digit) and his dad's age is represented by the digits "BA" (with B representing the tens digit and A representing the ones digit).
2) The problem tells us that the sum of their ages is 77. So, we can set up an equation: AB + BA = 77. Since AB and BA are the same number but with reversed digits, we can rewrite the equation as 10A + B + 10B + A = 77.
3) Simplify the equation: 11A + 11B = 77.
4) Divide both sides of the equation by 11 to get A + B = 7.
5) We also know that Julian is 27 years younger than his dad. So, A - B = 2.
6) Now, we have a system of equations: A + B = 7 and A - B = 2.
7) Solve the system of equations to find the values of A and B. We can do this by adding both equations together: (A + B) + (A - B) = 7 + 2. This simplifies to 2A = 9.
8) Divide both sides of the equation by 2 to get A = 9/2, which simplifies to A = 4.5.
9) Substitute the value of A back into one of the equations to solve for B. Let's use A - B = 2. Substitute A = 4.5: 4.5 - B = 2.
10) Subtract 4.5 from both sides of the equation to get -B = 2 - 4.5. This simplifies to -B = -2.5.
11) Multiply both sides of the equation by -1 to get B = 2.5.
Therefore, Julian's age is 45 years old.