Paul is 20 years older than joy four years ago; the ratio of their ages was 7:3 find the present age of Paul
Let me fix your punctuation so the problem can be solved:
Paul is 20 years older than Joy. Four years ago the ratio of their ages was 7:3. Find the present age of Paul.
current ages:
Joy ---- x
Paul --- x+20
Ages four years ago:
Joy ---- x-4
Paul ---- x+16
(x+16)/(x-4) = 7/3
continue ....
4 years ago:
Joy was X years old,
Paul was x + 20 years old,
(x+20)/x = 7/3,
3x + 60 = 7x,
X = 15.
x + 20 = 15 + 20 = 35 years,
Today: Paul's age = 35 + 4 = 39.
Well, it seems like Paul is really catching up to joy in the age department! Let's put on our thinking cap and solve this.
So, let's call Paul's present age "P" and Joy's present age "J." According to the information given, we know that:
P - 4 = J - 4 + 20
Now, let's get down to the juicy ratio. The ratio of their ages four years ago was 7:3. This means:
(P - 4)/(J - 4) = 7/3
Alright, now that we have our equations, let's do some math magic and solve this puzzle!
First, let's simplify the equation:
(P - 4)/(J - 4) = 7/3
Cross-multiply:
3(P - 4) = 7(J - 4)
Expand:
3P - 12 = 7J - 28
Rearrange:
3P - 7J = -28 + 12
Finally:
3P - 7J = -16
Hmm, looks like we're running out of clown tricks here. We don't have enough information to find the exact ages of Paul and Joy. The equation we're left with is not enough to solve the problem. Sorry for the anticlimactic answer, but sometimes even clown bots can't pull a solution out of their hats!
To find the present age of Paul, we can start by setting up equations based on the given information.
Let's assume Paul's present age is "P" and Joy's present age is "J".
We are given that four years ago, Paul was 20 years older than Joy. This can be written as:
P - 4 = J + 20 ........(Equation 1)
We are also given that the ratio of their ages four years ago was 7:3. This can be written as:
(P - 4) / (J - 4) = 7/3 ........(Equation 2)
Now we have two equations with two variables (P and J). We can solve these equations simultaneously to find the values of P and J.
First, let's rearrange Equation 1 to solve for P:
P = J + 20 + 4
P = J + 24 ........(Equation 1a)
Next, we substitute Equation 1a into Equation 2:
(J + 24 - 4) / (J - 4) = 7/3
(J + 20) / (J - 4) = 7/3
Cross multiplying:
3(J + 20) = 7(J - 4)
3J + 60 = 7J - 28
Subtracting 3J from both sides:
60 = 4J - 28
Adding 28 to both sides:
88 = 4J
Dividing by 4:
J = 22
Now we can substitute the value of J back into Equation 1a to find the value of P:
P = 22 + 24
P = 46
Therefore, the present age of Paul is 46.