SOLUTION: paddy is three times as old as Siobhana. Seven years ago, he was five times as old as Sibohana.How old is Paddy now?

Question 242785: paddy is three times as old as Siobhana. Seven years ago, he was five times as old as Sibohana.How old is Paddy now?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Start by defining your terms.
p = Paddy's age
s = Sibohana's age
Now we set up the givens:
p = 3s OR Paddy is 3 times Siobhana's age
p -7 = 5(s-7) OR 7 years ago, Paddy was 5 times Siobhana's age
Notice that we show BOTH p-7 and s-7 as their ages 7 years ago.
Substituting the value of p from the first equation into the second:
3s -7 = 5(s - 7)
Multiplying through the right side:
3s -7 = 5s - 35
Subtracting 3s from both sides:
-7 = 2s - 35
Adding 35 to both sides:
-7 + 35 = 28 = 2s
Dividing both sides by 2:
14 = s. Siobhana is 14.
We know from the setup that:
p = 3s, so p = 3(14) = 42. Paddy is 42.
Check your work!
Substitute the values into the second equation.
p - 7 = 5(s - 7)
42 - 7 = 5(14 -7)
35 = 5(7), which is true.
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