Paul is exactly 6 years older than Jane. The ratio of their ages is 5:3
How old is Paul?
Let's call Paul's age "P" and Jane's age "J".
From the given information, we have two equations:
P = J + 6 (Paul is 6 years older than Jane)
P/J = 5/3 (The ratio of their ages is 5:3)
We can use substitution to solve for the ages.
Substitute P in the first equation with J + 6:
J + 6 = J + 6
J = 0
Substitute J in the second equation with 0:
P/0 = 5/3
Since division by 0 is undefined, this implies that there is no solution to the problem.
Step 1: Let's assume Jane's age as "x".
Step 2: According to the given information, Paul is exactly 6 years older than Jane. So Paul's age would be x + 6.
Step 3: The ratio of their ages is given as 5:3. This means that the ratio of Paul's age to Jane's age is also 5:3.
Step 4: Setting up the proportion, we have (Paul's Age)/(Jane's Age) = 5/3. Substituting Paul's age (x + 6) and Jane's age (x) into the proportion, we get (x + 6)/x = 5/3.
Step 5: Cross-multiply the proportion to get 3(x + 6) = 5x.
Step 6: Distribute the 3 on the left side of the equation to get 3x + 18 = 5x.
Step 7: Subtract 3x from both sides of the equation to get 18 = 5x - 3x.
Step 8: Combine like terms on the right side of the equation to get 18 = 2x.
Step 9: Divide both sides of the equation by 2 to solve for x, which gives x = 9.
Step 10: Now that we know Jane's age is 9, we can find Paul's age by substituting it into the equation Paul's age (x + 6). Thus, Paul's age is 9 + 6 = 15.
Therefore, Paul is 15 years old.